Pre-Market Skills, Occupational Choice, and

Career Progression

Jamin D. Speer∗

Yale University

January 2014

Abstract

This paper develops a new theoretical and empirical framework for analyzing

occupational choice and career progression, focusing on the role of pre-labor market

skills in determining career outcomes. I propose a model of occupational choice in

which a worker’s skill vector determines his choice of occupation tasks. Skills grow

with experience through learning-by-doing in a way that may be related to the ini-

tial occupation. To obtain a rich account of pre-market skills and individual career

trajectories, I merge the NLSY79 and 97 with O*Net data on the task content of

occupations. I find that pre-market skills as measured by the ASVAB test scores

(math, verbal, mechanical, and science) and an interpersonal skill measure predict

the corresponding task content of the workers’ initial occupations, even after con-

trolling for general skill measures like education. I then ask how the relationships

between skills and occupations evolve as workers gain experience. Pre-market skills

have long-lasting effects on career outcomes. Career trajectories are similar across

worker skill types, implying that initial differences in occupation persist over the

course of a career. The change in the tasks performed by a typical worker over

the first 25 years of his career is equivalent to the difference in tasks associated

with about 2.3 years of education. I provide two policy-relevant applications of

∗Email: jamin.speer@yale.edu, Webpage: https://sites.google.com/site/jaminspeer/

1

this framework. First, I study the role played by pre-market skills in the differ-

ing occupational outcomes of men and women. The ASVAB scores account for

a portion of occupational gender gaps, including 70% of the gap in science and

engineering occupations. Occupational gender gaps also persist over the course of

a career. Second, I quantify the effect of layoffs on occupational attainment and

career trajectory. I find that a layoff erases about one-fourth of a worker’s total

career increase in task content, but within 3 years, this effect is typically undone.

1 Introduction

The question of why workers do the jobs they do is fundamental to understanding how

labor markets function. In this paper, I ask two questions. First, to what extent can pre-

labor market skills account for variation in occupation choice? Second, how persistent

are initial differences in occupation over the course of a career?

This paper develops a new theoretical and empirical framework for analyzing occu-

pational choice and career progression, focusing on the role of pre-labor market skills

in determining career outcomes. I develop a model which illuminates the relationships

between a worker’s skill set and his choice of occupation. Using a novel combination of

data on workers’ skill portfolios with data on the task requirements of their occupations,

I find a strong role for skills in the initial occupation choices of workers. I also show that

career trajectories are similar across workers, meaning that pre-market skills are impor-

tant determinants of both initial occupations and later career outcomes. I then apply

this framework to study two policy-relevant questions: the role of skills in accounting for

gender differences in occupation outcomes, and the effects of layoffs on career paths.

Studying the links between pre-market skills, occupation choice, and career trajectory

is difficult due to the data requirements. This paper combines rich data on workers’ skill

portfolios for a panel of individuals that I observe over several decades (the NLSY79 and

NLSY97) with data on the task requirements of their occupations (O*Net). The NLSYs

provide me with a set of pre-market skill measures (the ASVAB test scores) for a panel

of individuals whose careers I can see unfold over several decades. The O*Net data allow

2

me to determine what types of tasks individuals are performing at different stages of

their careers. Together, these data sources allow me to examine in detail how pre-market

skills and occupation choices interact in forming individuals’ careers. In particular, I can

ask how a worker’s test score in a given field (e.g., math) is related to the task content

of that field in his occupation, and how this relationship changes over the course of his

career.

I develop a model of occupational choice and career progression in which a worker is

characterized by a vector of skills and an occupation by a vector of tasks. Skills are the

abilities of the worker, either endowed or learned, while tasks are the activities required

in an occupation to produce output. The worker’s optimal choice of occupation depends

on how his skill vector matches with the tasks required in the occupation, as well as the

market returns to those tasks. A worker’s skills grow through learning-by-doing in a way

that may be related to his initial occupation choice.

The model has implications for both initial occupation choice and career trajectory.

Pre-market skills, including skills specific to one field and more general skills, should

predict initial occupation choice. As careers progress, initial differences in occupation

choice may widen, shrink, or persist perfectly over the course of a career depending on

how skill accumulation is related to the initial choice of occupation.

First, I find that pre-market skills as measured by the ASVAB components (math,

verbal, mechanical, and scientific aptitude), and an interpersonal skill measure, predict

the task content of the workers’ initial occupations, even after holding constant measures

of general skill such as education. Workers higher in verbal skill, for example, enter

occupations which use more verbal tasks, holding all else equal. It is not simply a

worker’s level of skill that determines occupation choice, but the types of skills he has.

I apply this framework to study the differing occupation outcomes of men and women.

I show that men are found in more mechanical- and science-intensive occupations, while

women are found in occupations requiring more math, verbal, and interpersonal tasks.

I ask if these gaps can be explained by differences in pre-market skills between men

and women. In the ASVAB, women score higher on the verbal tests, while men score

higher on the mechanical and science tests, particularly at the top of these distributions.

3

Differences in ASVAB scores account for a portion of occupational gender gaps, including

70% of the gender gap in science and engineering occupations. Including only the AFQT

score (a commonly used composite of the math and verbal ASVAB components) accounts

for only little of these gaps.

Second, having established the links between skills and initial occupation choice, I ask

how these relationships evolve as workers gain experience. I develop a method for describ-

ing career paths empirically by quantifying how the task content of a worker’s occupation

changes with experience. I show that career trajectories are similar across worker skill

types and across race and gender, implying that initial differences in occupation persist

over the course of a career. As careers progress, workers of all types increasingly move

to occupations which require more math, verbal, and interpersonal tasks, and fewer me-

chanical tasks. The change in the tasks performed by a typical worker over the first 25

years of his career is equivalent to the difference in tasks associated with about 2.3 years

of education.

I apply the career progression framework to study the effect of layoffs on a worker’s

career path. It is well known that layoffs can have persistent negative effects on earnings

(e.g., Jacobson, LaLonde and Sullivan (1993), von Wachter (2012)), but less is known

about the mechanisms behind this effect, including potential impacts on occupations

and career paths. I find that a layoff erases about one-fourth of a worker’s total career

increase in task content. However, that effect is short-lived. After 3 years, the effect of the

layoff on occupation content is mostly undone. On the other hand, the negative effects

of a layoff on wages outlast the effects on occupation tasks, suggesting that occupation

content is not the only mechanism driving these wage effects. The initial effect of a layoff

on occupation content can account for about 20% of the initial effect on wages.

These two applications of my framework – gender gaps in occupation outcomes and

the effects of layoffs – are quite different, which is a testament to the applicability of the

framework to a variety of policy-relevant questions.

While the NLSY (especially the NLSY79) has been used extensively by researchers,

my use of the ASVAB scores to analyze occupational sorting and career paths is novel.

The results show that pre-market skills in a variety of different fields play an important

4

role in the career outcomes of workers, including the differing occupational outcomes of

men and women. Utilizing the wider set of ASVAB scores, rather than just the AFQT

score, significantly improves our understanding of these outcomes.

The study of occupational choice has a rich history in economics, and economists have

long recognized skills an important determinant of these choices. Roy (1951) develops

a model in which workers have 2 skills, and comparative advantage and the returns to

skills determine which sector the worker enters. Heckman and Sedlacek (1985) present a

model which allows for multiple skills, both observed and unobserved, which have varying

usefulness in different jobs.1 Still, empirical evidence linking worker skill portfolios to

occupation characteristics is rare.

This paper builds on both Roy (1951) and Heckman and Sedlacek (1985). I consider a

broad set of worker skills and characterize occupations on a multi-dimensional continuum

of task content. I then combine data sources in a novel way to provide empirical evidence

on the relationships of workers’ skill vectors to occupation choice.

The economics literature has also documented that workers change occupations often

(e.g., Miller (1984), Kambourov and Manovskii (2008)). Economists have interpreted the

pattern of frequent job changes in many ways: as a search process for a better “match”

(Jovanovic (1979), Neal (1999)), as workers learning about their own skills (Gibbons,

Katz, Lemieux and Parent (2005), Papageorgiou (2012), James (2012)), as employers

learning which workers are worthy of promotions (Jovanovic and Nyarko (1997)), or as

evidence of skill accumulation (Rosen (1972), Sanders (2012)).

I contribute to the occupational choice and mobility literatures by developing a frame-

work linking pre-market skills to occupation choices over the course of a career, and by

combining data sources to quantify the effects of these skills. Instead of focusing on

the determinants of individual occupational changes, I focus on the broad patterns that

characterize career paths, and I ask whether skill measures predict deviations from these

broad patterns. Other types of models, particularly those that emphasize worker or

employer learning, are complementary with my framework. I provide a description of

1Blau et al. (1955) propose a broader occupational choice framework, which accounts for skills,personality traits, discrimination, and other factors. I consider only skills here, although I discuss howthese other factors may be affecting my results.

5

average career paths given worker characteristics, which will aid other researchers in in-

terpreting deviations from those broad trends, which may be due to workers learning

that they were not exactly right about their preferences or skills, or shocks to preferences

associated with marriage fertility, and other events.

A growing literature on the task content of occupations has made progress in inter-

preting occupational mobility patterns by examining the relationships between occupa-

tions (Poletaev and Robinson (2008), Gathmann and Schonberg (2010)). This literature

draws on new data sources which allow researchers to look inside the “black box” of

census occupation codes and descriptions (e.g., Yamaguchi (2010b), Yamaguchi (2012)).

By characterizing an occupation as a bundle of tasks, one can study the relationship of

different occupations and more meaningfully look at mobility patterns.

However, this literature has not to this point focused on understanding what types of

workers enter each type of occupation. In some cases, occupation tasks are used as a proxy

for the worker’s skills (Ingram and Neumann (2006), Robinson (2010)), but evidence on

sorting patterns is required to justify this assumption. By combining occupation task

data with data on a variety of pre-market skill measures, I provide some of this evidence.

While the occupation task literature provides an interpretation for individual occu-

pational changes, a framework for interpreting a worker’s entire career remains elusive.

A recent paper by Sanders (2012) merges the NLSY with O*Net data and interprets

changes in tasks over a career as a combination of skill accumulation and learning. He

does not consider the matching of skills to tasks. I add to this work by considering the

determinants of initial occupation choice and career trajectory jointly, and by providing

empirical evidence on how skills affect these patterns.

This paper also contributes to the literature on the effects of pre-market skills for

later outcomes. A series of papers by Heckman, including Heckman, Stixrud and Urzua

(2006), has shown that both cognitive and non-cognitive abilities have impacts on workers’

later outcomes. Neal and Johnson (1996), using the NLSY, show that AFQT scores can

account for much of the wage gap between blacks and whites. I add to this literature by

measuring the effects of a wide array of pre-market skill measures on occupation choices

and showing how those effects persist over the course of a career.

6

The paper proceeds as follows. Section 2 presents a model of occupational choice and

the determinants of career progression. Section 3 describes the data sources, and section

4 describes the empirical strategy. Sections 5 and 6 present the results, which include

applications of the occupation choice and career path framework. Section 7 concludes.

2 A model of occupational choice and career pro-

gression

Here I develop a model of how workers choose their occupations and how their careers

progress. I first present a one-period model in which a worker chooses an occupation to

maximize his wage. A worker is characterized as a vector of skills, and an occupation

as a vector of tasks. I assume that skills are constant at pre-market levels, and I char-

acterize the relationships between the worker’s skill vector and the content of his chosen

occupation.

Then, I allow skills to accumulate after labor market entry through learning-by-doing,

turning the choice of occupation into a dynamic problem. Skill accumulation is allowed to

depend on the worker’s initial occupation, implying that it also depends on the worker’s

initial skills. Career trajectories may therefore differ for workers of different skill sets,

and initial gaps in occupation may shrink, widen, or persist perfectly.

2.1 A one-period model of occupational choice

An occupation is characterized by a bundle of tasks, which are the technology of pro-

duction in an occupation. Tasks are a combination of activities and knowledge required

in production of an output. A worker is characterized by a set of skills, which are tal-

ents, abilities, and knowledge useful for performing tasks. Skills may be either specific or

general. A specific skill is only useful in performing a given task; an example might be

knowledge of how to operate a hand saw. A general skill is useful in performing any task.

An example of a general skill might be problem solving ability, which makes a worker

more productive in whatever task he is performing.

7

An occupation requires two types of tasks j and k. A worker has skills (sj,sk,sg). The

terms sj and sk denote specific skills, useful in performing tasks j and k, respectively,

while sg denotes general skill, useful for performing both j and k.2 General skill may be

correlated with specific skills, but is not a function of specific skills, and vice versa. A

worker chooses an occupation – a vector (j,k) – to maximize his wage.

Wages are determined by supply and demand for tasks. In Appendix A, I provide a

simple model of wage determination, based on Altonji and Rosenzweig (2007).3 Workers

use skills to perform tasks, which are the intermediate inputs used to produce output.

Firms sell output to the market, and demand for this output drives demand for tasks.

Labor markets are perfectly competitive spot markets, so that workers are paid their

marginal product in each period. The wage function is an equilibrium condition that

reflects (1) the demand for the final output that tasks are used to produce, (2) the

production function relating a worker’s skills and the tasks he performs to his output,

and (3) the supply of workers with each type of skill.

Worker i’s output x in occupation γ, which requires tasks jγ and kγ (e.g., math and

interpersonal activities), is

xiγ = f(sij, sik, sig; jγ, kγ).

The production function f has two key features. First, higher levels of each specific

skill makes a worker more effective in performing the associated task – sj for task j and

sk for task k. Second, higher general skill sg makes a worker more effective in performing

both tasks j and k. The production function has the same form for all occupations, and

only differs by the levels of j and k each occupation uses.

On the demand side, let us assume that the price of the output of an occupation can

be approximated by a flexible function of tasks j and k. Occupations differ only by the

levels of j and k that they require. For a suitable formulation of the production function

and of demand for output (see Appendix A), the following flexible log wage formulation

2In the empirical analysis, an occupation will require more than two types of tasks, and a worker willhave more than two types of specific skills. I use a two-task model here for ease of exposition.

3See Acemoglu and Autor (2011) for a more complete treatment of the supply and demand for tasks.

8

results for worker i in an occupation γ which uses task levels jγ and kγ:

ln(wiγ) = α1jγ − α2j2γ + α3sijjγ + α4kγ − α5k

2γ + α6sikkγ + α7sigjγ + α8sigkγ + α9jγkγ.

I suppress the i and γ subscripts going forward. The wage coefficients reflect a com-

bination of the worker’s production and demand for occupation output, and should not

be interpreted as technology parameters from a production function. Both demand for

output and the production function are assumed to be constant over time, so that the α

coefficients are constant.4

The first two terms show diminishing returns and increasing costs of fielding an oc-

cupation with a high level of task j. The third term reflects the complementarity of

specific skill sj and task j, which comes from the worker’s production function. The

next three terms are analogous to the first three for k. If skill-task complementarity is

more important for one task than another, α3 and α6 may differ. The seventh and eighth

terms reflect the complementarity of general skill and each task. If general skill raises

productivity in one task more than in another, α7 and α8 may differ.5 The first eight

coefficients are assumed to be positive.

A skill is not valuable unless it is applied to a task. If a worker with some skill sk

were to choose an occupation which uses none of task k, then he would not be paid for

his skill sk. Note also that the wage is zero when the worker chooses an occupation which

requires zero levels of j and k.6

The final term reflects how j and k are priced in equilibrium, which is determined by

the distribution of demand across occupations. If demand for output tends to be higher

in occupations which use higher levels of both tasks, then α9 > 0. If, on the other hand,

demand is higher for output of occupations that use one task or the other, but not high

4The expanded model in Appendix A discusses how changing demand conditions would affect thewage coefficients.

5The basic structure and intuition of the wage function are adapted from Altonji (2005), who analyzesthe choice of occupations along a single dimension.

6The wage in occupation γ is not generally equal to zero if the worker has zero skill. It is useful tointerpret the skills as deviations from the mean skill, so that the wage in occupation γ at sj = sk = sg = 0is the wage for the average worker if he chooses that occupation.

9

levels of both, then α9 < 0. When α9 > 0, I refer to the tasks as complements, and when

α9 < 0, I refer to the tasks as substitutes.7

A low-skill worker will find himself unproductive in a high-task occupation. In terms

of task j, the second term (−α2j2) ensures that not all workers will opt for the highest

j possible, while the third term (+α3sjj) and seventh term (+α7sgj) ensure that more-

skilled workers will choose higher-j occupations (ignoring effects of task substitutability).

Similar statements can be made for task k.8

2.1.1 Optimal task choices

A worker chooses an occupation – a (j,k) pair – to maximize his wage. I assume that

occupations have full support over (j,k). This is essentially a Roy (1951) model with

continuous occupation measures. The first order conditions are

α1 − 2α2j∗ + α3sj + α7sg + α9k

∗ = 0

α4 − 2α5k∗ + α6sk + α8sg + α9j

∗ = 0

which, after solving and substituting, lead to solutions of

j∗ =2α1α5 + α4α9 + 2α3α5sj + α6α9sk + sg(2α5α7 + α8α9)

4α2α5 − α29

(1)

k∗ =2α4α2 + α1α9 + 2α6α2sk + α3α9sj + sg(2α2α8 + α7α9)

4α2α5 − α29

. (2)

The solutions provide information about the relationships between each skill and its

7The term α9, then, is not a characteristic of the production function, but of demand. Alternatively,one could imagine that production itself is increasing or decreasing in the product of j and k. Theimplications of such a setup the same.

8An alternative formulation would include a time budget constraint for tasks. As I discuss in thedata section, my occupation task data do not distinguish between changes in task amount and tasklevel, making it difficult to interpret a budget constraint for tasks. The model I use here is similar toa formulation which omits the α7 and α8 terms and instead includes a budget constraint in which theworker’s general skill level serves as the constraint for how many tasks a worker may take on. Predictionsfrom such a model are nearly identical to the model I consider here.

10

“own” task, each skill and the other task, and general skill and each task.9 I discuss each

of these relationships separately.

2.1.2 Sorting: skills to tasks

First, the relationship between each specific skill and its associated task is positive.

∂j∗

∂sj=

2α3α5

4α2α5 − α29

> 0

∂k∗

∂sk=

2α6α2

4α2α5 − α29

> 0.

The effect of sj on j∗ is unambiguously positive, and is increasing in α3 (the degree

of complementarity between sj and j in production) and in α5, which reflects the degree

of diminishing returns to task k.

Second, the relationship of a specific skill with the other task depends on whether the

two tasks are substitutes or complements. Specifically,

∂j∗

∂sk=

α6α9

4α2α5 − α29

R 0

∂k∗

∂sj=

α3α9

4α2α5 − α29

R 0.

Because of the relationship of j and k in demand for output, a specific skill affects

the choice of both tasks, despite only being useful in its own task. The signs of these

relationships depend on the sign of α9. If two tasks are substitutes (α9 < 0), then each

skill affects the other task negatively. This is the logic of comparative advantage. If two

tasks are complements (α9 > 0), then each skill affects the other task (and its own task)

positively. These relationships highlight the need to consider the entire skill vector, not

just the own skill, in analyzing the worker’s choice of tasks.

9Throughout the analysis, I will assume that |α9| is small enough that the denominator is positive.

11

Third, the relationship between general skill sg and each task is ambiguous. The

derivatives are

∂j∗

∂sg=

2α5α7 + α8α9

4α2α5 − α29

R 0

∂k∗

∂sg=

2α2α8 + α7α9

4α2α5 − α29

R 0.

If the two tasks are complements, then the relationships are clearly positive; higher

general skill will raise the optimal choice of both tasks. Workers of higher general skill

would be found in higher-j, higher-k occupations. If, however, they are substitutes, the

relationship is unclear. General skill will negatively predict j and k, respectively, if

α9 <−2α5α7

α8

and

α9 <−2α2α8

α7

.

Intuitively, general skill may negatively predict a task if general skill is much more

helpful in performing the other task. Consider the case in which tasks j and k are

substitutes, and general skill is very helpful in task j and not as helpful in task k (α7

is large and α8 is small). Then it may be the case that general skill raises the optimal

choice of j but decreases the optimal choice of k. Workers of high general skill would be

found in high-j, low-k occupations.

I have assumed that occupations have full support over (j,k). In the case that general

skill is positively related to one task and negatively related to the other, there will be

very few workers found in occupations with high levels of both tasks or with low levels

of both tasks. Therefore, the observed support of occupations in (j,k) space will show

12

a negative correlation between j and k, and the high-j, high-k (and low-j, low-k) areas

will be sparsely populated. Occupations may not have full support over (j,k) because

of this. In other words, the actual distribution of j and k in available occupations is an

outcome of the model, but my assumption is that any (j,k) pair would be available if the

worker wanted to choose it.

2.1.3 What does the skill vector measure?

The vector (sj,sk,sg) refers to the worker’s skills at labor market entry. This includes

innate ability, parental investments, and educational investments, including possibly col-

lege attendance. Because these skills depend in part on educational choices made by the

worker, which may have been undertaken with specific occupations in mind, they are

potentially endogenous and should not be taken as randomly assigned to workers. In Ap-

pendix C, I provide a model of how a worker makes decisions about college investments

based on his pre-college skill set.

In this model of college choice, a worker observes his skill vector at the end of high

school and makes a decision about whether to attend college, what type of college to

attend, and what to major in. The model shows that higher-skill workers are more likely

to attend college, and that choice of major is positively related to skills a worker already

has (i.e., a worker high in sj is more likely to major in a field related to task j).10 If

this is true, then the skills at the time of labor market entry – which may include college

investments – are functions of the pre-college skills. Education increases a worker’s skills

in a way related to the skills he already had. Therefore, while the skill vector (sj,sk,sg)

is partially the product of a worker’s choices, they are choices made based on his earlier

skill set. I address this issue further in Section 5.2, where I discuss how to interpret my

results.

10In an ongoing project, I show empirical results that confirm these predictions. College major contentis closely related to a worker’s test scores measured before college.

13

2.2 Skill accumulation and career progression

I now turn to the dynamics of occupation choice over the course of a career. Workers

work for T periods and may choose a new occupation in each period at no cost. I denote

experience by t < T and assume that workers’ skills grow as follows:

sg,t+1 = sg,t + ψt

sj,t+1 = sj,t + µ0 + µ1jt

sk,t+1 = sk,t + π0 + π1kt.

Specific skills grow via learning-by-doing as well as an exogenous growth component.

General skills grow according to an experience profile ψt, which I assume is common

across all workers.11

Workers have the incentive to “invest” in their future skills by choosing higher values

of j and k than they otherwise would. The worker’s problem is now more complex, as

he maximizes the present discounted value of his wages instead of his one-period wage.

Because the choice of j in period t affects sj,t+1 and therefore jt+1 and kt+1, the problem is

also much more difficult to solve, and the solution is not as elegant as the static solution.

Recalling the one-period solution, we can now write the dynamic solution for j in the

form

j∗t =2α1α5 + α4α9 + 2α3α5sjt + α6α9skt + sgt(2α5α7 + α8α9)

4α2α5 − α29

+ It

= j∗static + It

where It is the investment term, or the difference between his one-period wage-maximizing

j and his optimal j in the dynamic problem.12 The worker now earns a lower wage in

11One could also imagine that general skill growth is influenced by the occupation choice of the worker.I assume that it is not in order to simplify the analysis.

12It > 0 for t < T . In period T , IT = 0 and the worker simply maximizes his final-period wage.

14

the early periods, sacrificing some pay for future skill accumulation. The logic here is

the same as in a Ben-Porath-type model (Ben-Porath (1967)), in which a worker chooses

each period how much to produce and how much to invest in skills. Here, there is no time

allocation decision for the worker, but his choice of occupation tasks determines both his

wage and his future skill growth.

I am primarily interested in the implications of these skill growth patterns for career

task progression and for the persistence of initial differences in occupation choice. First,

consider the case in which specific skills do not grow (µ0 = µ1 = π0 = π1 = 0). In this

case, as workers gain experience, their general skills are the only thing changing. The

effect of experience on the worker’s choice of tasks will be the same as the effect of general

skill sg in the one-period problem (which is ambiguous). In this case, initial differences

in occupation persist perfectly, because the experience profile of general skill is the same

for all workers.

If specific skills grow via learning-by-doing (µ1 > 0 and π1 > 0), then workers who

begin their careers in higher-j occupations – which would include workers with higher

initial levels of sj and sg (if sg has a positive relationship with j) – will see their skill sj

grow faster than those of other workers, which will translate into faster growth of task j

in their occupations. Initial differences in occupation choice should widen as experience

increases.13

It could also be the case that skill growth is negatively related to initial occupation

(µ1 < 0 and π1 < 0) if there are diminishing returns to skill accumulation. In this case,

initial occupation gaps will shrink over the course of a career.14

2.3 Summary of empirical implications

There are two sets of empirical implications from the model. First, I look at the effects

of skills on the initial occupation’s tasks. The one-period solution for j from equation

13These implications are made stronger if the two tasks are substitutes and weaker if they are com-plements. Even for strong complements, however, initial differences grow if µ1 > 0 and π1 > 0.

14Because skill growth is linearly related to occupation in this simple model, having µ1 < 0 andπ1 < 0 would imply that occupation paths for workers who start in different occupations cross at someexperience level. While this is possible, I am focused here on the period of experience over which thegaps would be shrinking.

15

(1) was15

j∗ =2α1α5 + α4α9 + 2α3α5sj + α6α9sk + sg(2α5α7 + α8α9)

4α2α5 − α29

,

which can be written as

j∗ = β0 + β1sj + β2sk + β3sg

where

β1 =2α3α5

4α2α5 − α29

β2 =α6α9

4α2α5 − α29

β3 =2α5α7 + α8α9

4α2α5 − α29

.

The model implies that β1 > 0 and the signs of β2 and β3 are ambiguous, depending on

α9 and other parameters.16

The second set of implications comes from the career progression section of the model.

The question is whether initial gaps in occupation choice widen, shrink, or persist per-

fectly over the course of a career. The answer depends on the relationship of skill growth

to the worker’s occupation. In the model, skill accumulation is as follows:

15Although the one-period solution is not the true relationship if skills grow over time, it providesan approximation to motivate the empirics. The same qualitative implications hold for the dynamicsolution.

16Here, there is a one-to-one mapping between skills and task choices. In reality, worker preferences,search frictions, omitted task measures, and other factors will also contribute to workers’ choices ofoccupations. This will cause there to be variation in skills within occupation.

16

sg,t+1 = sg,t + ψt

sj,t+1 = sj,t + µ0 + µ1jt

sk,t+1 = sk,t + π0 + π1kt.

The experience profile ψt of general skill is assumed to be common to all workers.

Recall that the effect of general skill on occupation choice is ambiguous, so this means

that the way tasks change with experience if general skill is growing is also not clear. If

skill growth is positively related to occupation (µ1 > 0 and π1 > 0), then initial gaps will

widen with experience. If µ1 < 0 and π1 < 0, then initial gaps will shrink. If µ1 = π1 = 0,

then initial gaps persist perfectly.

3 Data

To evaluate the implications of the model, I require data with a rich set of worker skill

measures and individual career trajectories, as well as data on occupation content. I use

the NLSY for the worker information and O*Net for the occupation information.

3.1 NLSY79 and NLSY97

The NLSY79 and NLSY97 are nationally representative panel surveys whose respondents

were aged 14 to 22 and 12 to 16, respectively, at the start of the surveys and have been

followed through the present. The NLSY is ideal for this project for two reasons. The

first reason is its panel structure; the NLSY79 covers several decades of workers’ careers,

while the NLSY97 covers the early-career outcomes of its respondents. In each survey

year, workers provide information on three-digit census occupation.17

The second key advantage of the NLSY is the inclusion of the Armed Services Vo-

cational Aptitude Battery (ASVAB) tests, which were taken by NLSY79 respondents in

17The NLSY97 respondents have been interviewed annually since 1997. The NLSY79 respondentswere interviewed annually from 1979 to 1994 and biennially since 1994.

17

1981 and NLSY97 respondents in 1999. The ASVAB covers ten subjects: general science,

arithmetic reasoning, word knowledge, paragraph comprehension, numerical operations,

coding speed, auto and shop information, mathematics knowledge, mechanical compre-

hension, and electronics information. This allows me to observe a worker’s proficiency

level in a variety of subjects with relevance to different types of occupation tasks. I

restrict most of my analysis to workers who took the ASVAB before entering the labor

market, which includes about two-thirds of the NLSY79 and almost all of the NLSY97.

For these workers, the ASVAB scores can be interpreted as pre-labor market skills.

While the NLSY79 alone would be sufficient for answering my research questions, my

analysis is enhanced by including the NLSY97. The NLSY97 respondents are younger

on average at the time of the ASVAB tests, and almost all of these workers take the

tests before entering the labor market. This adds to my sample size for analysis of

initial occupations and helps produce a more balanced sample.18 The disadvantage of

the NLSY97 is that it only follows workers through the early part of their careers. To

estimate longer career trajectories, I also need the NLSY79.

The ASVAB was developed by the United States military in 1968 and was adopted

by all U.S. military branches in 1976. To enlist in the military, a recruit must achieve

a minimum score on the AFQT, which is a combination of the math and verbal compo-

nents of the ASVAB. The wider set of subject tests in the ASVAB is used to determine

eligibility for various military occupations. For example, the U.S. Air Force defines an

“electrical” composite score as the sum of the math knowledge, electronics information,

and general science tests. To work in ground radar systems, avionic systems, or space

systems operations, a soldier must achieve a certain score on this composite.19 Studies

from within the military have shown that the relevant ASVAB score categories predict

performance in their associated occupations (Sims and Hiatt (2001), Welsh and Kucinkas

(1990)).

I use the ASVAB scores to analyze the sorting patterns of civilian workers into oc-

18Restricting the NLSY79 to workers who entered the labor market after taking the ASVAB producesa sample weighted toward more educated workers.

19A complete list of military occupation requirements is available at http://www.military.com/join-armed-forces/asvab.

18

cupations. Given the military’s use of these tests, this is a natural use of the data in

the NLSY. Each military branch combines the scores in different ways to assign workers

to occupations, so I create my own four composite categories: math, verbal, mechan-

ical, and science. I define the math score as the mean of the mathematics knowledge

and arithmetic reasoning tests; verbal as the mean of word knowledge and paragraph

comprehension; mechanical as the mean of auto and shop information and mechanical

comprehension; and science as the mean of general science and electronics information.20

I also utilize a self-reported measure of sociability as a measure of interpersonal “skill”.

NLSY79 respondents were asked in the 1985 survey to rate their own sociability, with

four possible answers. Because sociability is not the same thing as interpersonal skill, I

will be cautious in interpreting the results using this measure.21

This gives me a five-dimensional specific skill vector: math, verbal, mechanical, sci-

ence, and interpersonal skill. I will use years of education as my primary measure of

general skill.22 Panel A of Appendix Table 1 shows the correlation matrix of the six skill

measures. The ASVAB scores are all positively correlated with education, suggesting

that they contain information about general skill as well as specific skill. In regressions

to evaluate the relationships of skills to tasks, the model suggests that I should control

for general skill and all specific skills. The coefficient on a test score in that regression

is the effect of the test score holding education fixed. I interpret this as the effect of the

specific skill, holding constant general skill.

I consider observations only after the worker has made a full transition to the labor

market, which I define as being out of school for two consecutive interview rounds and

20Results are similar when electronics information is included in the mechanical composite rather thanthe science composite.

21Level of sociability, even if measured accurately, is not the same as interpersonal skill for a varietyof reasons. The possible answers are also problematic and may convey value judgments; only 1.5 percentof respondents say they are “extremely shy”. Unfortunately, no comparable measure is available inthe NLSY97. For all NLSY97 respondents, I set interpersonal skill equal to the mean value from theNLSY79.

22Education likely contains information about both general skill and specific skills, depending on whatthese workers chose to study in school. Appendix C provides a model justifying the use of education as ameasure of general skill. In empirical results I do not show here, I find that the ASVAB scores are strongdeterminants of college major content. This suggests that the information that would be conveyed aboutspecific skills by education is largely captured by the ASVAB scores themselves.

19

being employed in the first of those two years. I define experience as years since the

transition to the labor market began.23 I exclude observations while workers are still

in school, because the model implies that the only source of skill growth once a career

begins is from the occupation. If a worker is accumulating skill in school, I consider those

pre-market skills.

I exclude from most of my analysis workers who transitioned to the labor market in

1981 or earlier (for NLSY79) and 1999 or earlier (for NLSY97), because these are the

years the respondents took the ASVAB tests. This eliminates about one-third of the

NLSY79 and about one-tenth of the NLSY97. A small number of respondents without

valid ASVAB scores are dropped. I also drop the military subsample of the NLSY79.

I use data from 1982 to 2010 in the NLSY79 and 2000 to 2010 in the NLSY97.

Summary statistics for the NLSY79 and NLSY97 are shown in Table 1. Because I only

observe the NLSY97 respondents for a few years, and the respondents with high education

for even fewer years, my NLSY97 observations have lower experience and education on

average. All test scores and the interpersonal skill measure are standardized separately

by quarter-year of birth to adjust for both age and potential education at the time of

taking the test, as suggested by Cascio and Lewis (2006).

3.1.1 What do ASVAB scores measure?

NLSY respondents took the ASVAB tests between ages 14 and 24. The tests represent

the worker’s skills at the time of the test, which include, among other things, inherited

and innate ability, parental investments, and educational inputs and choices. Some of the

inputs into ASVAB scores may reflect choices made by the worker, such as which high

school courses he took, which college major he chose, and which occupation he entered

or planned to enter. I cannot separate the effects of innate ability from the effects of

parental investments or a worker’s pre-test choices and preferences.

Figures 1 and 2 display the distributions of ASVAB scores in my four composite

subjects separately for men and women and for whites, blacks, and Hispanics (the dahsed

23This definition of labor market transition is similar to those used by Farber and Gibbons (1996) andSchonberg (2007). Results are similar with different definitions. About 5% of workers return to schoolafter making this transition. I keep counting their experience even when they have returned to school.

20

vertical lines denote the mean for each group). There are substantial racial and ethnic

differences in ASVAB scores, with whites scoring highest on all four measures. Neal and

Johnson (1996) find that AFQT differences between blacks and whites can account for

much of the race gap in wages. They emphasize, however, that this does not imply that

there are innate differences between blacks and whites. Rather, the test score gaps may

be influenced the many factors listed above as well as (rational) expectations of future

labor market discrimination.

There are also ASVAB score differences by gender, as seen in Figure 1. The math

and verbal scores are similar for men and women, with men scoring slightly higher in

math and women scoring slightly higher in verbal. Altonji and Blank (1999) and others

have noted that including AFQT cannot explain much of the wage gap between men

and women.24 However, men score significantly higher on the mechanical and verbal

components of the ASVAB. I will return to this in section 5.1 as an application of the

occupation choice framework, but it is worth noting here that these gender gaps in ASVAB

scores may also be the product of discrimination, parental expectations and investments,

and expectations of future discrimination. They should not be taken as innate ability

differences. Evidence from Fryer and Levitt (2010) suggests that gender differences in

math test scores widen as students spend more time in school, suggesting a role for factors

other than innate ability in opening these gaps. While I do not find large differences in

math scores here, the same principle may apply for the other tests.

One useful check is to measure the gender gaps in test scores for the sample of NLSY

respondents who took the tests before age 19. This eliminates the effects of college

investments. For instance, boys are more likely to study science in college than girls; if

this is driving the test score differences by gender, then the gender gaps in scores will be

smaller for the age-restricted sample. In fact, the gender test score gaps are 80-90% as

large for the younger test-takers as they are for the full sample. The vast majority of the

gender gap in scores, then, is being driven by pre-college-age factors. This certainly does

not rule out educational investments differing by gender, but it does suggest that these

24To my knowledge, no paper has attempted to explain occupational differences between men andwomen using the AFQT.

21

investments must be occurring earlier than college.

3.2 O*Net

I also require data on tasks required in each occupation. For this, I use O*Net, the

Department of Labor’s successor to the Dictionary of Occupational Titles. It contains

detailed information on dozens of activities, skills, knowledge, and abilities used in each

occupation. I call these measures “tasks”.

A total of 159 tasks are rated for each occupation. It is useful for my purposes to

summarize the data by a smaller number of factors. I require occupation-level25 measures

of math, verbal, mechanical, science, and interpersonal tasks to match the worker skill

data from the NLSY. I choose a set of tasks for each category (based on their descriptions

given by O*Net), and for each set of tasks, I extract a single factor using principal

component analysis.2627 I am able to categorize 26 of the 159 task measures in one of

my five skill categories. The remaining task information is not used. The measures I use

and their descriptions from O*Net are in Appendix B.

I standardize my five composite task measures to be mean 0 and variance 1, weighting

by employment in the combined 1980 and 1990 decennial censuses. Table 2 provides the

composite task measures for a selected set of occupations, in standard deviation units.28

The first five occupations listed are the highest-scoring in each category: mathematicians

for math, writers and authors for verbal, and so on.

25Occupation-level task measures should be thought of as averages for that occupation. Using worker-level data, Autor and Handel (2013) show that there is substantial variation in task performance withinoccupation.

26Each task gives an “importance” and “level” measure; I use the importance measure, which gives amore intuitive ranking of occupations. Results are generally not sensitive to this choice, as the importanceand level measures are highly correlated.

27In general, there are two approaches one can use to deal with the dimensionality of the task vector.The first is to use factor analysis to identify a set of “underlying factors” required for each occupation– for example, general intelligence, fine motor skills, etc. This is the approach taken in Poletaev andRobinson (2008) and Robinson (2010). The other approach is to choose task categories ex-ante andthen determine which tasks fit in each category. This approach, taken by Autor and Handel (2013),allows more flexibility in answering different research questions. My approach is a combination of thetwo techniques, but is closer to the latter.

28O*Net measures are at the level of SOC codes, while the NSLY occupations are at the 3-digit Censuscode level. I crosswalk the two using the mapping provided by Ruggles et al. (2010).

22

Appendix Table 2 shows the correlations between each task and an occupational

earnings measure, which is the occupation fixed effect from a regression in the March

CPS of log earnings on worker characteristics and occupation dummies.29 Math and

verbal tasks are most strongly correlated with occupational earnings, with science and

interpersonal also positively correlated with occupational earnings. Mechanical tasks are

slightly negatively correlated with occupational earnings.30

Panel B of Appendix Table 1 shows the correlation matrices for occupation tasks.

Math, verbal, and interpersonal tasks are positively correlated with each other, while all

of these are negatively correlated with mechanical tasks. Mechanical and science tasks

are highly positively correlated in occupations.

4 Empirical implementation

There are two primary questions to analyze: the relationship of skills to initial occupation

and how these relationships change with experience (career progression).

For initial occupation choice, I will regress each of the five task measures (math,

verbal, mechanical, science, and interpersonal) for worker i in an occupation using tasks

j and k on all four test scores, the interpersonal skill measure, and education, restricting

to early-career observations.31 The regression equation is

jit = λ0 + λ1sij + Λ2Sik + λ3educi + νt + εit

29The worker characteristics I include in this regression are dummies for seven education categories,gender, race, a quadratic in potential experience, and year fixed effects. I restrict to workers aged 35 to59 working full-time and to years 1980 to 1999.

30These correlations are not the true return to the task, because workers may select into occupationsbased on unobservable characteristics. When I regress the occupational earnings measure on the taskmeasures, the coefficient on mechanical tasks is positive but small and insignificant.

31I also regress the sum of all five tasks on the skill measures and education to give a sense of theeffect of skills on the total level of tasks. I do this to provide a benchmark measure of the total effectof education on tasks, which I will use later to compare with the effect of experience on tasks. Analternative would be to use a wage-weighted sum of the five tasks, which would put more weight onmath and verbal tasks. Here I use the sum for simplicity.

23

where i denotes the worker, j denotes the task level in his occupation (for math, verbal,

mechanical, etc.), sj is his test score or skill in field j, Sk is the vector of other specific

skills (all specific skills other than skill sj), and νt are year fixed effects. The term εit is

an error term, which may include a worker’s idiosyncratic preferences for the occupation

task.

The year fixed effects are included to control for differing economic conditions and

demand for tasks in different years. In the model, I assumed that demand for output

across occupations was constant, meaning the α wage coefficients were constant.32 How-

ever, the data are drawn from a number of different years, and demand conditions may

have changed over the sample period.

I estimate these regressions on workers with experience 0 to 2, to estimate the impact

of pre-market skills on early-career occupations.33 I also exclude workers who took the

ASVAB after transitioning to the labor market. I cluster the standard errors at the

worker level to allow for arbitrary correlation in errors within a worker across time.

To study career progression and how the skill-task relationships change with expe-

rience, I will estimate career paths – how each task changes with experience – and ask

whether these paths are different for workers of different skill.

I do this by regressing each task on a quadratic in experience, the skill measures,

and interactions between experience and education, test scores, race, and gender.34 The

regression equation is

jit = φ0 + φ1expit + φ2exp2it + Φ3Xi + Φ4Xiexpit + demandjt + υit

where Xi is a vector of race, gender, and ability variables, including education and the

32The model in Appendix A discusses how changing demand for output in different occupations couldaffect the α coefficients.

33I use this definition of early career instead of just the initial occupation to achieve a larger samplesize. Results are similar when I restrict only to the first observation per worker.

34This method of describing career progression – estimating how task measures change with experience– is similar in spirit to the methodology used by Yamaguchi (2010a). My task measures are more detailed,however, and are linked to the worker skill characteristics. This allows me to test career path differencesacross workers in the manner predicted by the model.

24

ASVAB scores (so Xi includes the skills (sj,sk,sg)).35 Because only the less educated

workers are observed at very high levels of experience, I restrict to observations with 25

or fewer years of experience and again exclude those who entered the labor market before

taking the ASVAB tests.

To control for changing demand for tasks over time, I would like to include year fixed

effects. However, with only a few cohorts, I have little variation to separately identify

year and experience effects. Instead, I construct a demand measure demandjt for each

task in each year. In the March CPS from 1979 to 2010 (the years covered by my sample),

for workers aged 25 to 45, I regress each task measure on a set of education dummies,

gender, race, a cubic in potential experience, and year fixed effects. The year fixed effect

is my measure of demand for that task in that year. I include the demand measure for

all five tasks in this regression, because changing demand for one task may also affects

the choices of other tasks.

5 Results: Occupational Choice

Table 3 shows the results of the regressions of early-career occupation tasks on skills.

There are several things to note. First, the coefficients on the diagonal show that for

all five tasks, the associated skill positively predicts the task. A one standard devia-

tion increase in the math ASVAB score leads to a 0.178 standard deviation rise in math

task content in the occupation. The other score-task relationships are similar in magni-

tude, except for mechanical, which is larger. The interpersonal skill measure’s effect on

interpersonal tasks is also positive and significant, though smaller.

Second, general skill (education) is positively related to math, verbal, and interper-

sonal tasks, and negatively related to mechanical tasks. Using the model to interpret

this, the usefulness of general skill in performing mechanical tasks must be lower than

its usefulness for math and verbal tasks. Furthermore, mechanical tasks must be sub-

stitutes with math, verbal, and interpersonal tasks.36 Overall, one year of education is

35Gender and race are included here because, as I show in the next section, these factors influenceinitial occupation outcomes as well.

36Another possible interpretation of these results is that education is positively related to omitted

25

associated with 0.278 higher total tasks; I will refer back to this number as a benchmark

for quantifying career progression later.37

Third, the relationships between skills and other tasks vary. Verbal and math tasks are

complements, as each skill positively predicts the other task. Mechanical and science tasks

are also complements. On the other hand, math and mechanical tasks are substitutes, as

each skill negatively predicts the other task. These results are consistent with the effects

of education as well.38

Utilizing the multi-dimensional skill vector instead of only a single measure (e.g.,

education or AFQT) improves our ability to understand occupation choice, particularly

for mechanical and science tasks, two types of skill not covered by the AFQT. Mechanical

skill also has a strong impact on math and especially verbal tasks, and is an important

omitted variable if not included.

5.1 Application: race and gender gaps in occupation outcomes

The results of Table 3 give us a better understanding of why workers are found in different

occupations. To further illustrate the usefulness of this framework, I now apply it to study

race and gender gaps in occupation content.39

Tables 4a and 4b40 show the results of regressions of each task on education and

dummies for male, black, and Hispanic, with no specific skill measures (but with year

effects), again restricting only to the early years of the career and using the same sample

variables (e.g., intelligence) that predict going into certain types of jobs and not others for reasons otherthan complementarity or substitutability of tasks.

37Note that education is not strongly related to science tasks. This is because occupations high inscience content tend to be in two categories: those associated with highly educated workers (engineers,scientists, etc.) and those associated with less-educated workers (electricians, repair workers, etc.)

38Although I have excluded workers who entered the labor market before taking the ASVAB tests,results for these regressions are almost identical when they are included, suggesting that the first fewyears of work experience may not have large effects on test scores.

39See Altonji and Blank (1999) for a summary of the literature on race and gender in the labor market.They show that men and women are found in different types of occupations – women in clerical andservice occupations, for example – and that blacks and Hispanics are found in less-skilled occupations.Women may also be in occupations with lower promotion possibilities (Paulin and Mellor 1996) andlower value to the firm (Schumann et al. 1994). In some cases, “blind” hiring procedures have beenshown to increase women’s probability of being hired (Goldin and Rouse 2000), providing evidence thatat least some of the gender differences in occupation choice are due to discrimination in hiring.

40I spread these regressions over 2 tables for space reasons.

26

criteria and clustering of standard errors at the worker level as in Table 3. There are

substantial race and gender gaps in each type of task. Females’ occupations are higher

in math, verbal, and interpersonal content, while males are found in occupations which

require much more science and mechanical tasks.41 Relative to whites, blacks are found

in occupations which require fewer math, verbal, science, and interpersonal tasks.

Can ASVAB scores explain any of these differences? Recall that Figure 1 plots the

densities of each test score separately for men and women. The gender gaps in mechanical

and science scores are large; men score 0.54 and 0.35 standard deviations higher than

women in mechanical and science, respectively. These differences are especially large at

the top of the distribution. About 20% of men score higher than the 99th percentile of

women on the mechanical component. Math and verbal scores also differ slightly across

gender, with women scoring about 0.10 standard deviations higher in verbal on average

(significant at the 1% level) and men scoring 0.03 standard deviations higher in math

(significant at the 10% level). The math and verbal differences largely even out to leave

only small gender differences in AFQT. Answers to the interpersonal skill question are

not significantly different for men and women.42

Recall also that Figure 2 plots the densities of each test score for whites, blacks, and

Hispanics. Neal and Johnson (1996) show that AFQT scores explain much of the black-

white wage gap. The figure shows that whites score higher than blacks and Hispanics on

all of the tests, and the average racial/ethnic gaps are about the same for each test.

I first ask if the AFQT score alone can explain the race and gender gaps in occupation

tasks. In Tables 4a and 4b, the second column for each task adds the standardized

AFQT score to the race and gender dummies. All of the racial gaps are explained or

over-explained by including the AFQT score. This is consistent with the results on wages

from Neal and Johnson (1996). However, adding AFQT does little to account for the

41The fact that women are in higher-math occupations may be surprising. The median observationsfor men and women have roughly the same math content, but the mean is higher for women. This isbecause men have much more mass in the lower tail of math occupations, while mass in the upper tailis roughly similar across men and women.

42Large gender gaps in the mechanical and science scores exist in both the NLSY79 and the NLSY97,but the gaps are smaller in the NLSY97. The average male advantage (in standard deviations) inmechanical and science scores, respectively, are 0.80 and 0.45 in the NLSY79 and 0.36 and 0.24 in theNLSY97.

27

gender task gaps.

The third column for each task in Tables 4a and 4b replaces the AFQT with the whole

set of ASVAB measures and the interpersonal skill measure. These skill measures account

for 17%, 21%, and 11% of the gender gaps in mechanical, science, and interpersonal tasks,

respectively. Because some scores have strong effects on “other” tasks, gender gaps in

each test score do not just account for the own-task gap. Although the interpersonal skill

measure is similar across men and women, including all five skill measures still explains

a modest portion of the gap in interpersonal tasks, largely because the mechanical score

negatively predicts interpersonal tasks.

Policy discussions about gender gaps in occupation outcomes often focus on particular

sets of occupations dominated by one gender, such as STEM (science, technology, engi-

neering, and mathematics) occupations.43 The test score distributions in Figure 1 show

gender differences in both means and variances, suggesting that these scores may explain

a larger portion of gaps for occupations drawing from the tails of these distributions. In

particular, men dominate the top of the mechanical and science test distributions.

I repeat the gender gap analysis for three particular groups of occupations with large

and well-known gender gaps: teachers (secondary and below), construction occupations,

and all scientists and engineers.44 Again, I include year dummies to control for changing

conditions over time. These are probit regressions, and I report the marginal effects

rather than the regression coefficients.

Table 5 displays the results for these selected occupation groups. Unsurprisingly, con-

struction workers and scientists and engineers are more likely to be male, while teachers

are more likely to be female. The AFQT score explains almost none of the gender gaps for

teachers and construction workers, and 24% of the gap among scientists and engineers.

Adding the wider set of ASVAB scores accounts for a much larger portion of all three

gaps, including 70% of the gender gap in science and engineering occupations. This

is for two reasons. First, it is helpful to separately enter the math and verbal scores,

which have opposing effects on the probability of entering science and engineering, rather

43See, for example, The White House (2012).44In my sample, males constitute 18% of teachers, 97% of construction workers, and 80% of scientists

and engineers.

28

than bundling them in AFQT. Second, the mechanical and science scores, in which men

perform significantly better, are positive predictors of going into these occupations.4546

Again, it is important to emphasize that race and gender differences in ASVAB scores

should not be taken as indicators of differences in innate ability. The ASVAB scores are

also likely a product of preferences, parental investments and expectations, educational

choices, discrimination, and expectations of future discrimination. With regard to gender,

girls and boys may be encouraged from a young age to enjoy and invest in different

activities, which could lead to test score gaps in teenage years. Fryer and Levitt (2010)

show that gender gaps in math scores in the U.S. open up only after students have

started school.47 Brown and Corcoran (1997) and Altonji (1995) show that boys and

girls take different types of high school courses in the U.S., particularly in vocational

areas (boys are more likely to take industrial arts courses, while girls are more likely to

take commercial arts courses), which again may be a product of skills, preferences, and

other factors.48 Other factors, such as the gender of the instructor in certain courses,

may also influence the achievement of boys and girls differentially (Dee (2007), Carrell,

Page and West (2010), Hoffmann and Oreopoulos (2009)).

5.2 Interpretation of ASVAB scores and effects on occupations

My results to this point suggest that skills formed by ages 14 to 22 have strong effects

on the types of occupations workers enter. These skills are a function of everything that

has happened up to that point in the worker’s life, including parental investments and

45I include education in all of these regressions, because while education partially reflects choices madeby the worker, the same is true for the ASVAB scores. If education is not included, results (not shownhere) are similar; the ASVAB scores account for almost 80% of the science and engineering gap.

46While these regressions are pooled across the NLSY79 and NLSY97, there is heterogeneity in effectsacross the two surveys. Both the gender gap in science and engineering and the degree to which ASVABscores can account for this gap are smaller in the NLSY97. In the later survey, ASVAB scores accountfor about half of the gender gap in science and engineering. However, a full comparison between the twoNLSYs is not possible yet, because the younger NLSY97 respondents may still be in graduate programsthat lead to science and engineering occupations.

47I note again here that I do not find large math score differences across gender in the ASVAB. However,the principle of test score gaps widening as students get more schooling may apply to mechanical andscience tests as well.

48These patterns may be changing over time. Goldin, Katz and Kuziemko (2006) document improve-ment over time in girls’ preparation for college relative to boys.

29

educational choices of the worker. The latter is potentially problematic; it may be that

desired occupation is driving educational investments, which shows up in the test scores.

One way to test for the importance of educational investments in driving the effects

is to take advantage of the structure of the NLSY surveys; respondents took the ASVAB

tests at different ages, allowing me to observe skills at various levels of education. Specif-

ically, I can restrict to workers who took the ASVAB tests prior to age 19 – that is, prior

to college investments having an effect. Though I do not show them here, all results are

similar for this sample. This includes the gender and race/ethnicity results. The gender

test score gaps, for instance, are 80-90% as large for the age-restricted sample as for the

full sample.

I conclude that the skills formed by age 14 to 18 have strong and (as I show below)

long-lasting effects on occupational outcomes of workers. These skills are likely still

influenced by educational choices, but they are at least not driven by college investments.

I cannot separate effects of innate ability, parental investments, and educational choices.

What I can say is that the skills formed by these ages are highly predictive of future

outcomes, including differential outcomes by race and gender.

6 Results: Career Progression

6.1 Skill-task relationships over the course of a career

Having established the relationships between skills and tasks in the initial occupations, I

now ask how those relationships change as workers gain experience. Do initial differences

in occupation (which are partially driven by skills) widen, shrink, or persist perfectly over

the course of a career?

In Table 6, I regress each task measure on a quadratic in experience, all skill mea-

sures, race and gender dummies, and the skill, race, and gender variables interacted with

experience. These regressions also include the task demand measures described in section

4 to control for changing demand conditions over time. I focus first on the specific skill

measures. For four of the five skills, there is no evidence that the task gradient is related

30

to the worker’s level of pre-market skill. For example, the math test score has a large

positive effect on math tasks initially, and this effect is almost perfectly stable over the

course of a career. The exception is the verbal category (column 2), for which workers

with higher verbal test scores see faster growth in verbal tasks as they gain experience.

Education, which has a large initial effect on tasks, also affects the task gradients.

Somewhat surprisingly, more educated workers see slower growth in most tasks. Taking

the coefficients in column 6 (on the sum of tasks), a worker with 4 more years of edu-

cation would see his task advantage eliminated in 15 years (holding all other measures

constant).49

The substantial gender differences in initial occupation seem to persist almost per-

fectly over the course of a career, controlling for the skill and race measures. Men do

close some of the gap in interpersonal tasks as they gain experience – in 20 years, about

a third of this difference would disappear – but the other gender task gaps are stable as

experience grows. Blacks seem to have different experience paths from whites and His-

panics, but some of the interactions are positive while others are negative. On the overall

sum of tasks measure, the interaction between black and experience is not significant.

Table 6 suggests that most of the interactions have small or insignificant effects on

tasks, but because many of the skill variables are correlated (e.g., education and test

scores, or gender and verbal test scores), it is difficult to see how career paths differ for

the average worker of each type.

In Figures 3 through 5, I graph estimates of career paths separately by gender, race,

and education level, to provide a visual reference for the information contained in Table

6.50 To produce these figures, I estimate the experience path of each task separately by

group, including worker fixed effects instead of controlling for other skill measures. This

accounts for all characteristics of the worker, both observed and unobserved, and allows

us to compare the relevant groups (e.g., men vs. women) holding all other characteristics

fixed. I estimate these paths on a set of eight experience category dummies, instead of

49It is important to emphasize that these are partial effects. Highly educated workers also have highverbal test scores, for example, and the interaction of verbal scores and experience has a positive effecton task growth that would oppose the negative effect of the education-experience interaction.

50Here, education is divided into three categories: high (16 years and above), medium (13 to 15 years),and low (12 or fewer years).

31

a quadratic, to allow more flexibility. The intercept term in the graphs is the average of

the fixed effects for that group.51

Initial occupation differences between men and women widen slightly with experience

for all five tasks. For instance, the average gap in science tasks between men and women

is 0.653 standard deviations initially; after 25 years, it is 0.731 standard deviations. The

math gap grows from 0.125 standard deviations (in favor of women) to 0.160. However, in

most cases, the initial gender gaps in occupation tasks are far larger than any differential

changes over the course of a career.

Racial differences in occupation are largely stable over the course of a career. The

average gap in math tasks between whites and blacks is 0.254 standard deviations ini-

tially; after 25 years, it is 0.257 standard deviations. Differences by education are also

fairly stable, with the exception of mechanical tasks, for which the initial gaps are nar-

rowed considerably. Appendix Table 3 reports, for race, gender, and education level, the

estimated average gaps at 0, 5, 10, 20, and 25 years of experience for each task.

Overall, there does not seem to be a consistent relationship between the factors that

affect initial occupation and the speed of task growth over the course of a career. Some

initial gaps widen, while others shrink, but in all cases, the vast majority of the initial

gap remains after 25 years of experience. The implication of these findings is that pre-

market skills (and other characteristics) have long-lasting effects on occupation outcomes.

Even after 25 years of experience, a worker’s ASVAB scores are strong predictors of his

choice of occupation. Race, gender, and education also remain important throughout the

worker’s career.

51These regressions also include the task demand measures. For these regressions, I also includeworkers who took the ASVAB after entering the labor market. These workers were excluded in the priorresults. I include them here because they help produce a more balanced sample to estimate effects athigher levels of experience. Without them, the sample is weighted more haavily toward workers withhigher education, which makes it difficult to estimate task effects at high levels of experience. Whenthese workers are excluded from these regressions, estimates at low levels of experience are similar, butthe estimates at high levels of experience are very imprecise. Also, when estimating average career pathsby group, I am not concerned about the effects of work experience on test scores, which was the reasonfor excluding these workers from prior regressions. Appendix Table 8 has summary statistics for thisexpanded sample.

32

6.2 Alternative explanations for similar career paths across ed-

ucation level

It is somewhat surprising that high-skilled workers do not see faster occupational pro-

gression. Here I focus on the interactions of education and experience, which had small

negative effects on tasks in the regressions of Table 6. The model interprets this as work-

ers of different education levels learning their skills at similar rates. I now discuss several

alternative explanations.

One explanation is that correlates of productivity that are easily observable to em-

ployers (such as education) become less important over time as employers learn about

harder-to-observe elements of ability, such as the ASVAB test scores.52 However, I do not,

in general, find that the ASVAB scores have an increasing effect on occupation content,

so something else must be driving my results.

A second possible reason for the lack of a higher experience gradient for more educated

workers is the occupational coding system, which may code low-skill occupations in more

detail than high-skill occupations. Highly educated workers may be upgrading their

task requirements without changing 3-digit occupation codes. Evaluating this possiblity

would require a detailed analysis of the distribution of workers across occupations, which

is beyond the scope of this paper.

A third possibility is that some high-education workers are in the highest-task occupa-

tions, where they are unable to upgrade any further. A mathematician (the highest-math

occupation) cannot upgrade his math task content even if his general or math skill in-

creases, because no higher-math occupation exists.53 If this is true, then the average high-

education worker will appear not to be upgrading his tasks faster than a low-education

worker, even if his skills are growing faster.

To investigate this possibility for math tasks, I find the 99th, 90th, 50th, 10th, and

1st percentiles of math tasks for each experience level, separately for the high-education

(16 and above) and low-education (12 and below) samples. I then regress each percentile

52The employer learning framework of Altonji and Pierret (2001) is one example of a model that wouldimply this pattern if applied to occupational attainment.

53A mathematician may upgrade his math task content within occupation by taking on more mathtasks (or more difficult math tasks), but this would not show up in the occupation codes.

33

on experience. If it is true that high-education workers’ task growth is not faster because

some workers are in “top-task” occupations, then I expect to see the median values

increasing faster for the high-education sample but the high-percentile values increasing

more slowly.

Appendix Table 4 has the results, which are mixed. The 99th percentile of math

tasks for the high-education group starts at the 98th percentile of occupations in terms

of math (roughly the level of an aerospace engineer), so it would be difficult for these

workers to move to higher-math occupations.54 The top percentiles for college graduates

actually show a decrease in math tasks with experience, which is consistent with these

workers being unable to increase their task content through occupation changes; the top

percentiles for the low-education sample do not show this pattern.

However, slower growth for the highly educated workers is not just found at the top

of their distributions; the median growth is also slower for college graduates than for the

low-education workers. The median college graduate is not near the top of the math

occupation distribution, so it is unlikely that he is constrained from moving to higher-

math occupations. The slower growth for highly educated workers is not only at the top

of the distribution, where a “task ceiling” might be affecting the results. While such

a ceiling may be part of the story, it cannot completely explain the lack of faster task

growth for more-skilled workers.

6.3 Average career paths

The results of section 6.1 suggest that there are relatively small differences in career paths

across different types of workers. It is useful now (and for the application that follows)

to quantify the degree of change in occupation tasks over a career for the average worker.

To control for the effects on tasks of both observables (education, test scores, etc.) and

unobservables, I estimate the career paths of each task for the pooled sample using worker

54This is particularly true because of possible educational requirements for entering top-level occupa-tions. These requirements are not included in the model, but in reality, it would be difficult for a workerto move into an occupation which usually requires an advanced degree.

34

fixed effects. I again control for the task demand measures described in section 4.55 The

regression equations are

jit = Φ1expcategoryit + ηi + demandjt + ξit.

Table 7 has these results. Math, verbal, and interpersonal tasks grow substantially

with experience for the average worker. Science tasks grow slightly, and mechanical tasks

decline with experience. Verbal and interpersonal tasks, the two tasks most strongly

associated with general skill in the sorting regressions, grow the most, suggesting that an

increase in general skill is the dominant force driving career task progression.56

To provide a benchmark for the degree of progression in occupation tasks over the

course of a career, I also regress the sum of the five tasks on the experience categories

in column 6. The sum of tasks grows with experience; a typical worker with 25 years of

experience is performing 0.641 standard deviations more total tasks than he did when

he first entered the labor market. Recall from Table 3 that one year of education is

associated with 0.278 higher total tasks. This implies that 25 years of career progression

in occupations is equivalent to the effect of about 2.3 years of education.

To help interpret these career patterns, it is useful to connect the task measures to

specific types of occupations. In the O*Net data, many management and supervisory

occupations are high in math, verbal, and interpersonal tasks, the tasks that workers

move toward as they gain experience. Figure 6 shows the fraction of workers in man-

agement of supervisory occupations at each value of experience, separately by education

level. Consistent with the occupation choice results, workers with more education are

55For these regressions, as in Figures 3 through 5, I also include workers who took the ASVAB afterentering the labor market to achieve a more balanced sample.

56Appendix Table 5 repeats this regression without the task demand measures. Results are qualita-tively similar, but the estimated task changes without the demand measures are about 50% larger. It isevident that some of the realized career task changes of these workers was driven by changing demandfor tasks as their careers progressed. Appendix Table 6 looks at this another way, comparing the earlycareers of the NLSY79 and NLSY97. They are similar except for mechanical and science tasks. Beaudry,Green and Sand (2013) suggest that demand for “manual” tasks was falling in the 1980s and 1990s butrising in the 2000s. This could explain why the early-career mechanical task paths of the two surveysare different, again suggesting that demand conditions play a role in determining career paths.

35

more likely to be in management occupations. 57 The experience paths are striking; all

education groups move into management and supervisory positions more as they gain

experience.

How much of the observed career paths could moves into management explain? In

Appendix Table 7, for each education group separately, I find the average change in

tasks that accompanies a move into a management occupation, and ask how much of

the average total task change such a move can account for.58 Particularly for the lower

education groups, moves into management occupations can account for a large portion

of the total career change in tasks.

The other thing to note from this table is that even within the category of manage-

ment and supervisory occupations, workers of different education level are performing

different tasks. Among managers, highly educated workers perform more math and ver-

bal tasks and fewer mechanical tasks. The task differences across education levels (see

Table 3) is only partially explained by a higher fraction of more educated workers being

in management occupations.

A (partial) interpretation of career paths involving moves to management occupations

is also consistent with career progression frameworks other than mine. A notable example

is a stepping-stone model (Jovanovic and Nyarko (1997)), in which firms learn about

workers’ abilities and promote those of higher ability. However, my results suggest that

for this type of model to be true, what firms learn about workers must be orthogonal to

both education and test scores, because these measures do not predict task growth (see

Table 6). This is possible but seems unlikely.

57The relationship is not monotonic if the education groups are more disaggregated. Those withexactly 16 years of education are more likely to be managers than those with more than 16 years.

58For this comparison, I estimate experience paths of each task separately by education group andcompare the coefficient on the 25-year experience category with the average change in tasks associatedwith a move into management. Because moves to management may be influenced by changing demandconditions over time, the appropriate comparison between management moves and overall task growthis to not include the task demand measures when estimating the experience profiles, so these measuresare excluded from these regressions.

36

6.4 Application: The effect of layoffs on career paths

Having established the task content of a typical career trajectory, I now apply this frame-

work to study the effects of layoffs on career paths. It is well known that workers who

are laid off suffer large and persistent earnings losses (Jacobson et al. (1993), Gibbons

and Katz (1991), von Wachter (2012)), but less is known about the mechanisms driving

this effect. At least some of the earnings effect is likely due to the effect of layoffs on

occupation quality, but the short- and medium-term effects of layoffs on occupations and

career paths are not well-understood.59

My contribution is to quantify both the initial and longer-term effects of layoffs on

occupational attainment in the context of a career path. I have shown that a typical

career is characterized by an increase in most types of tasks and a decline in mechanical

tasks. If a worker is laid off while on this typical career path, one might wonder if he

is permanently thrown off the path, or if he is able to recover in the years following

the layoff. The answer may shed light on the mechanisms that lead to such persistent

earnings losses from a layoff.

In this section, I do two things. First, I quantify the immediate and subsequent effects

of layoffs on occupational attainment by re-estimating career paths with indicators for

when a worker was laid off. Second, I follow the same procedure for wages instead of

occupations, and ask how much of the negative effect of layoffs on wages can be explained

by an effect on occupations.

I follow Krashinsky (2002) in identifying layoffs in the NLSY data sets. Workers

are asked the reason they left previous jobs, which allows me to differentiate between

voluntary and involuntary moves.60 NLSY respondents may report multiple jobs in a

year, but I only consider the current or most recent job in each survey, as occupation

codes are often missing for the other jobs. If a worker is employed and reports being

59Poletaev and Robinson (2008) find that displaced workers generally move to occupations whichrequire less skill, and that the wage loss associated with a layoff is positively related to the degree of thisoccupational downgrade. However, they do not consider the longer-term effects of a layoff on occupation,such as whether the worker is able to recover to an occupation similar to his pre-layoff occupation. Seealso Gathmann and Schonberg (2010) for analysis using German data.

60I categorize both plant closings and firings as layoffs. Temporary jobs that have ended are notcounted as layoffs.

37

laid off from the prior year’s occupation, then the pre-layoff and post-layoff occupations

are simply last survey’s “current” job and this survey’s current job, respectively. If the

respondent is unemployed and reports being laid off from his most recent job, then that

job is the pre-layoff job, and the next year’s “current” job is the post-layoff job.

Is a worker who is laid off able to rebound and reach his previous career path, or is he

permanently left behind? Table 8 investigates this by regressing each task (and the sum

of tasks) on the set of experience category dummies, the task demand measures, worker

fixed effects, and dummies for “laid off in the past year”, “laid off 2 years ago”, “laid off

3 years ago”, and “laid off 4 years ago”.

The results show that a layoff has a substantial initial effect on the task content of

occupations. The initial effect of a layoff is to move the worker into an occupation which

uses lower levels of math, verbal, science, and interpersonal tasks. The initial effect of

a layoff on the sum of tasks is a loss of 0.16 standard deviations in total tasks, which is

about one-fourth of the total 25-year increase in task content estimated in Table 7, which

was 0.641 standard deviations.61

However, the effect of a layoff on occupation content is short-lived. About 40% of the

effect of a layoff on occupation tasks is gone after one year, and virtually all of the effect

is gone after three years. I do not find any evidence here that laid-off workers are pushed

permanently off their occupational career path.62

It is useful to connect these results to the well-known effects of layoffs on wages. How

much of the wage effect can be explained by this effect on occupations? Table 9 repeats

the layoff regressions with the log real wage as the dependent variable in column 1. The

effect on wages decays as the worker recovers from the layoff, but the effect of a layoff

on wages is still significant 4 years after the layoff, or after the effect on occupation has

worn off.

In columns 2 and 3, the dependent variable is the predicted wage from regressions

of wages on the skill measures, education, and task measures (the dependent variable in

61The estimates of career changes in tasks are slightly smaller here, because they do not includethe first few years of the NLSY79, which are associated with fast task growth. This regression thusunderestimates total career task growth.

62In results I do not show here, I find that the effects of layoffs on occupation content are generallyunrelated to the worker’s skills.

38

column 3 also adds interactions between education and the task measures and each task

measure with its “own” skill measure). The results from these two columns suggest two

things. First, the effect of a layoff on occupation tasks accounts for a modest portion –

perhaps 20% – of the total effect of a layoff on wages. Second, the effects of a layoff on

the occupation-predicted wage dissipate faster than the actual effect on wages. This is

consistent with the results for occupation task measures in Table 10. One explanation

for the greater persistence of wages than occupation characteristics is that workers may

enjoy rents in their pre-layoff jobs, and even if they return to the same type of occupation

post-layoff, they lose these rents (Schmieder and von Wachter 2010).

6.5 The support of occupations in task space

In the model, I assume that occupations have full support over tasks j and k, so that

a worker may choose any bundle of tasks. In the data, this assumption is not accurate.

Figure 7 shows scatter plots of math tasks with each of the other four tasks. Each dot is

one census three-digit occupation, with the size of each dot representing employment in

that occupation in the pooled NLSY data.

There are several empty regions in these plots: high math/low verbal, high math/high

mechanical, and low math/high science, for example. A worker could not choose these

bundles, because no such occupation exists. This provides an alternative interpretation

for the results of Table 3. Math and mechanical tasks may be negatively correlated in

workers’ choices simply because they are negatively correlated in available occupations.

However, the model itself could be used to think about why these particular regions

of the task distributions are empty. In the model, if two tasks are complements, then

occupations which use high levels of both tasks are more lucrative for workers. If two

tasks are substitutes, then a worker would prefer to not enter an occupation which uses

high levels of both task. Using this intuition, even if available occupations did have full

support over tasks, it is possible that no worker would choose occupations in certain

regions, and these regions would therefore appear empty. For example, if math and

verbal tasks are complements, then workers choosing high levels of math tasks would

also want to choose high levels of verbal tasks (and vice-versa). In this case, the high

39

math/low verbal and low math/high verbal occupation spaces would be empty or sparsely

populated, as they are in Figure 7.

7 Conclusion

This paper develops a new theoretical and empirical framework for analyzing occupational

choice and career progression. Combining data on workers’ pre-market skills with data

on the task content of their occupations, I document a strong role for these skills in

determining workers’ occupational outcomes, both initially and later in their careers.

Using this framework, I show that pre-market skills can account for some of the race and

gender gaps in occupation content, particularly at the top of the science task distribution.

Gender gaps in ASVAB scores account for 70% of the gap in science and engineering

occupations.

Furthermore, it is not simply the level of pre-market skills which matters, but the

type of skills. Whether a labor market entrant is of higher ability in science or reading

and writing has implications for his choice of occupation throughout his career. Skills

are multi-dimensional, and the dimensions matter. This is particularly relevant in un-

derstanding the differing occupation outcomes of men and women.

As careers progress, workers increasingly move to occupations which require more

math, verbal, and interpersonal tasks, and fewer mechanical tasks. Career patterns

are remarkably common across all types of workers, implying that initial differences in

occupation choice persist over the course of a career. This means that the effects of

pre-market skills on career outcomes are long-lasting.

Applying this framework to study career disruptions, I find that a layoff erases about

one-fourth of a worker’s total career increase in task content, but this effect is short-lived.

After 3 years, the effect of the layoff on occupation content is mostly gone, and does not

persist as long as the effect of a layoff on wages.

The framework that I have developed can also be extended to consider postsecondary

education, as discussed in Appendix C. By characterizing college majors as a vector of

course types, similar to the way I have characterized occupations as a vector of tasks, one

40

can study the relationship of a worker’s ASVAB test scores to the types of educational

investments he makes, and then link those investments to occupation choice.

I have used this paper’s framework to study two major policy-relevant issues: race and

gender gaps in occupation content and the effects of layoffs. The framework is useful for

studying a variety of other questions. For example, one could use it to study the effects of

labor market polarization (Autor, Levy and Murnane (2003)) on workers who begin their

careers in occupations high in routine tasks. The occupation choice framework could also

be used to study migration decisions of workers to regions which demand more of the

skills they possess, or how occupation choices respond to immigration or trade shocks.

Future research will explore additional applications.

41

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46

Tables and Figures

Figure 1:

0.1

.2.3

.4D

ensi

ty

−4 −2 0 2 4St. deviations

Men Women

Math

0.1

.2.3

.4D

ensi

ty

−4 −2 0 2 4St. deviations

Men Women

Verbal

0.1

.2.3

.4.5

Den

sity

−4 −2 0 2 4St. deviations

Men Women

Mechanical0

.1.2

.3.4

Den

sity

−4 −2 0 2 4St. deviations

Men Women

Science

Dashed vertical lines denote means

Test score densities by gender

47

Figure 2:0

.1.2

.3.4

.5D

ensi

ty

−4 −2 0 2 4St. deviations

White Black

Hispanic

Math

0.2

.4.6

Den

sity

−4 −2 0 2 4St. deviations

White Black

Hispanic

Verbal

0.2

.4.6

Den

sity

−4 −2 0 2 4St. deviations

White Black

Hispanic

Mechanical

0.1

.2.3

.4.5

Den

sity

−4 −2 0 2 4St. deviations

White Black

Hispanic

Science

Dashed vertical lines denote means

Test score densities by race/ethnicity

48

Figure 3:−

.3−

.2−

.10

.1T

ask

0 5 10 15 20 25Exp

Men Women

Math

−.4

−.2

0.2

.4T

ask

0 5 10 15 20 25Exp

Men Women

Verbal

−.6

−.4

−.2

0.2

.4T

ask

0 5 10 15 20 25Exp

Men Women

Mechanical

−.6

−.4

−.2

0.2

Tas

k

0 5 10 15 20 25Exp

Men Women

Science

−.4

−.2

0.2

.4.6

Tas

k

0 5 10 15 20 25Exp

Men Women

Interpersonal

Estimated paths of tasks by gender

49

Figure 4:−

.3−

.2−

.10

.1T

ask

0 5 10 15 20 25Exp

Whites Blacks

Math

−.4

−.2

0.2

Tas

k0 5 10 15 20 25

Exp

Whites Blacks

Verbal

−.1

5−

.1−

.05

0T

ask

0 5 10 15 20 25Exp

Whites Blacks

Mechanical

−.2

5−

.2−

.15

−.1

−.0

5T

ask

0 5 10 15 20 25Exp

Whites Blacks

Science

−.2

−.1

0.1

.2.3

Tas

k

0 5 10 15 20 25Exp

Whites Blacks

Interpersonal

Estimated paths of tasks by race

50

Figure 5:−

.4−

.20

.2.4

Tas

k

0 5 10 15 20 25Exp

Low Med

High

Math

−.5

0.5

1T

ask

0 5 10 15 20 25Exp

Low Med

High

Verbal

−.6

−.4

−.2

0.2

Tas

k

0 5 10 15 20 25Exp

Low Med

High

Mechanical

−.2

5−.2

−.1

5−.1

−.0

5T

ask

0 5 10 15 20 25Exp

Low Med

High

Science

−.4

−.2

0.2

.4.6

Tas

k

0 5 10 15 20 25Exp

Low Med

High

Interpersonal

Estimated paths of tasks by education

51

Figure 6:0

.1.2

.3.4

.5F

ract

ion

0 10 20 30Experience

Educ >= 16 Educ 13 to 15Educ <= 12

Fraction in management or supervisory occupations

52

Figure 7:−

20

24

Mat

h

−2 −1 0 1 2Verbal

Math and verbal

−2

02

4M

ath

−2 −1 0 1 2 3Mechanical

Math and mechanical

−2

02

4M

ath

−2 0 2 4Science

Math and science

−2

02

4M

ath

−3 −2 −1 0 1 2Interpersonal

Math and interpersonal

Each circle is a 1990 census 3−digit occupation, size−weighted by employment in the pooled NLSY data sets.

Task scatterplots

53

Table 1

Summary statistics

NLSY79 NLSY97

Mean Stdev Mean Stdev

Male 0.52 0.50 0.51 0.50

Black 0.28 0.45 0.25 0.44

Hispanic 0.16 0.36 0.19 0.40

Education 13.90 2.35 13.09 2.50

Experience 9.89 7.68 3.46 2.68

Math score 0.08 1.00 -0.01 0.93

Verbal score 0.07 0.96 -0.02 0.93

Mechanical score 0.09 1.00 -0.00 0.87

Science score 0.08 0.99 -0.01 0.93

Interpersonal skill 0.00 0.98 – –

Math tasks 0.01 1.00 -0.14 1.00

Verbal tasks 0.09 0.99 -0.17 0.96

Mechanical tasks -0.13 0.95 -0.15 0.93

Science tasks -0.08 0.97 -0.21 0.86

Interpersonal tasks 0.12 0.98 0.06 0.94

Total observations 43,824 29,480

Number of ID 3,966 4,834

Notes: The sample includes workers who transitioned

to the labor market in 1982 or later (for NLSY79) and

2000 or later (for NLSY97). Experience is years since

the transition began. The task measures refer to the

current or most recent job.

54

Table 2

Task measures for selected occupations, in standard deviation units

Task Measures

Occupation Math Verbal Mechanical Science Interpersonal

Mathematicians 4.08 0.11 -1.38 0.64 -1.83

Writers and authors -0.97 2.45 -1.25 -0.44 0.13

Elevator installers -0.50 -0.30 2.46 1.86 0.58

Aerospace engineers 2.11 1.28 -0.29 3.49 -0.01

Mgrs of service organizations 0.92 1.42 -1.00 -0.93 2.35

Economists 1.61 1.28 -1.44 -0.79 0.61

Chief executives 1.06 1.90 -1.33 -0.64 2.20

Electricians 0.74 -0.40 1.79 1.91 -0.10

Construction supervisors 0.63 -0.02 0.81 1.04 0.73

Registered nurses 0.55 1.23 -0.51 -0.89 1.78

Clergy 0.30 1.57 -0.70 -0.88 2.32

Lawyers 0.07 2.22 -1.51 -0.92 2.15

Automobile mechanics -0.48 -0.74 1.52 1.15 -0.33

Waiters -1.16 -0.99 -1.01 -0.98 0.47

Barbers -1.23 -1.00 -0.46 -0.80 0.69

Construction laborers -1.63 -1.41 0.70 0.99 -0.98

Notes: See Appendix B for the O*Net task categories used to create these task

measures. The first five occupations are the highest-task occupations in math, verbal,

mechanical, science, and interpersonal tasks, respectively. These are 3-digit 1990

census occupations. All task measures are in standard deviations.

55

Table 3

Early-career occcupational choice regressions

(1) (2) (3) (4) (5) (6)

math tasks verbal tasks mech. tasks science tasks interp. tasks sum of tasks

math score 0.178*** 0.136*** -0.113*** 0.023 0.071*** 0.295***

(0.016) (0.014) (0.014) (0.016) (0.014) (0.039)

verbal score 0.007 0.197*** -0.324*** -0.312*** 0.257*** -0.175***

(0.018) (0.015) (0.015) (0.017) (0.016) (0.043)

mechanical score -0.031** -0.137*** 0.302*** 0.276*** -0.180*** 0.230***

(0.015) (0.013) (0.014) (0.015) (0.013) (0.037)

science score 0.016 -0.075*** 0.154*** 0.170*** -0.102*** 0.163***

(0.019) (0.016) (0.017) (0.019) (0.017) (0.045)

interpersonal skill 0.014 0.028** -0.019* -0.003 0.041*** 0.061*

(0.013) (0.011) (0.011) (0.013) (0.012) (0.031)

education 0.094*** 0.165*** -0.090*** -0.009** 0.118*** 0.278***

(0.005) (0.004) (0.004) (0.004) (0.004) (0.012)

Constant -1.426*** -2.427*** 1.134*** -0.082 -1.614*** -4.416***

(0.066) (0.058) (0.060) (0.060) (0.061) (0.162)

Observations 22,487 22,487 22,487 22,487 22,487 22,487

R-squared 0.131 0.333 0.197 0.093 0.196 0.172

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: The sample is restricted to workers with 0 to 2 years of experience who took the ASVAB tests before

entering the labor market. Math, verbal, mechanical, and science skill are measured by ASVAB test scores.

Interpersonal skill is the answer to a question of how sociable the worker is, and is only available in the NLSY79;

it is set to 0 (the mean for the NLSY79) for all NLSY97 observations. See Appendix B for the O*Net task

categories used to create these task measures. All skill and task measures are in standard deviations. The

standard errors are clustered at the worker level.

56

Table 4a

Race and gender gaps in occupation content

(1) (2) (3) (4) (5) (6)

math tasks verbal tasks

Male -0.059*** -0.059*** -0.075*** -0.350*** -0.350*** -0.311***

(0.018) (0.017) (0.020) (0.015) (0.015) (0.017)

Black -0.152*** -0.036 -0.029 -0.137*** -0.015 -0.042**

(0.021) (0.023) (0.023) (0.018) (0.019) (0.020)

Hispanic -0.019 0.052** 0.056** 0.089*** 0.165*** 0.147***

(0.024) (0.025) (0.025) (0.021) (0.021) (0.021)

education 0.132*** 0.100*** 0.094*** 0.201*** 0.167*** 0.163***

(0.004) (0.005) (0.005) (0.003) (0.004) (0.004)

AFQT 0.153*** 0.163***

(0.013) (0.011)

math score 0.172*** 0.118***

(0.016) (0.013)

verbal score -0.016 0.107***

(0.018) (0.015)

mech. score -0.019 -0.073***

(0.016) (0.013)

science score 0.035* -0.003

(0.019) (0.016)

interp. skill 0.015 0.033***

(0.013) (0.011)

Constant -1.865*** -1.524*** -1.393*** -2.708*** -2.346*** -2.267***

(0.062) (0.067) (0.069) (0.052) (0.057) (0.058)

Observations 22,487 22,487 22,487 22,487 22,487 22,487

R-squared 0.117 0.128 0.133 0.340 0.353 0.357

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: The sample is restricted to workers with 0 to 2 years of experience who took the

ASVAB tests before entering the labor market. Math, verbal, mechanical, and science skill

are measured by ASVAB test scores. Interpersonal skill is the answer to a question of how

sociable the worker is, and is only available in the NLSY79; it is set to 0 (the NLSY79 mean)

for all NLSY97 observations. See Appendix B for the O*Net task categories used to create

these task measures. The standard errors are clustered at the worker level.

57

Table 4b

Race and gender gaps in occupation content (continued)

(1) (2) (3) (4) (5) (6) (7) (8) (9)

mechanical tasks science tasks interpersonal tasks

Male 0.670*** 0.670*** 0.559*** 0.612*** 0.612*** 0.482*** -0.482*** -0.482*** -0.428***

(0.015) (0.015) (0.016) (0.016) (0.016) (0.017) (0.015) (0.015) (0.018)

Black -0.025 -0.106*** -0.030 -0.128*** -0.107*** -0.024 -0.049*** 0.042** 0.005

(0.017) (0.018) (0.019) (0.017) (0.019) (0.020) (0.019) (0.020) (0.021)

Hispanic -0.090*** -0.141*** -0.094*** -0.102*** -0.089*** -0.038* 0.053** 0.110*** 0.087***

(0.021) (0.022) (0.022) (0.021) (0.022) (0.022) (0.021) (0.022) (0.022)

education -0.109*** -0.087*** -0.084*** 0.004 -0.002 -0.003 0.140*** 0.115*** 0.114***

(0.003) (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.004) (0.004)

AFQT -0.108*** 0.028** 0.120***

(0.011) (0.012) (0.011)

math score -0.088*** 0.044*** 0.051***

(0.014) (0.015) (0.014)

verbal score -0.169*** -0.179*** 0.137***

(0.015) (0.017) (0.016)

mech. score 0.173*** 0.165*** -0.084***

(0.014) (0.015) (0.014)

science score 0.038** 0.074*** -0.012

(0.016) (0.019) (0.017)

interp. skill -0.028** -0.010 0.047***

(0.011) (0.013) (0.011)

Constant 1.076*** 0.837*** 0.798*** -0.502*** -0.439*** -0.384*** -1.657*** -1.389*** -1.361***

(0.050) (0.056) (0.056) (0.054) (0.058) (0.058) (0.054) (0.059) (0.061)

Observations 22,487 22,487 22,487 22,487 22,487 22,487 22,487 22,487 22,487

R-squared 0.250 0.256 0.272 0.129 0.130 0.150 0.225 0.233 0.238

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: The sample is restricted to workers with 0 to 2 years of experience who took the ASVAB tests before entering the labor

market. Math, verbal, mechanical, and science skill are measured by ASVAB test scores. Interpersonal skill is the answer

to a question of how sociable the worker is, and is only available in the NLSY79; it is set to 0 (the NLSY79 mean) for all

NLSY97 observations. See Appendix B for the O*Net task categories used to create these task measures. The standard errors

are clustered at the worker level.

58

Table 5

Race and gender gaps in selected occupations

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Teachers Construction occupations Scientsts and engineers

Male -0.022*** -0.022*** -0.018*** 0.047*** 0.047*** 0.042*** 0.009*** 0.007*** 0.003**

(0.002) (0.002) (0.002) (0.003) (0.003) (0.003) (0.001) (0.001) (0.001)

Black -0.001 -0.002 -0.004** -0.007*** -0.009*** -0.007*** -0.004*** 0.000 0.002

(0.002) (0.002) (0.002) (0.001) (0.001) (0.001) (0.001) (0.001) (0.002)

Hispanic -0.000 -0.002 -0.003 -0.006*** -0.007*** -0.006*** -0.004** -0.001 -0.000

(0.002) (0.002) (0.002) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)

education 0.007*** 0.007*** 0.007*** -0.004*** -0.003*** -0.003*** 0.004*** 0.002*** 0.002***

(0.001) (0.001) (0.001) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

AFQT -0.002** -0.003*** 0.005***

(0.001) (0.001) (0.001)

math score -0.001 -0.001 0.006***

(0.001) (0.001) (0.001)

verbal score 0.002 -0.004*** -0.004***

(0.002) (0.001) (0.001)

mech. score -0.002 0.004*** 0.002***

(0.002) (0.001) (0.001)

science score -0.004** -0.000 0.001

(0.002) (0.001) (0.001)

interp. skill -0.002 -0.000 -0.001

(0.001) (0.001) (0.001)

% of gender gap

accounted for 0% 17% 1% 11% 24% 70%

Observations 22,487 22,487 22,487 22,214 22,214 22,214 20,759 20,759 20,759

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: The sample is restricted to workers with 0 to 2 years of experience who took the ASVAB tests before entering the

labor market. These are probit regressions, in which I report the marginal effects. Math, verbal, mechanical, and science

skill are measured by ASVAB test scores. Interpersonal skill is the answer to a question of how sociable the worker is, and is

only available in the NLSY79; it is set to 0 (the NLSY79 mean) for all NLSY97 observations. See Appendix B for the O*Net

task categories used to create these task measures. Teachers do not include postsecondary teachers. The standard errors are

clustered at the worker level.

59

Table 6

Skill-task relationships over the course of a career

(1) (2) (3) (4) (5) (6)

math tasks verbal tasks mech. tasks science tasks interp. tasks sum of tasks

exp 0.011*** 0.024*** 0.006** 0.009*** 0.004* 0.054***

(0.003) (0.002) (0.002) (0.002) (0.002) (0.007)

exp2 -0.000 -0.000*** -0.000* -0.000** -0.000 -0.001***

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

math score 0.171*** 0.113*** -0.089*** 0.041*** 0.056*** 0.293***

(0.016) (0.014) (0.014) (0.015) (0.014) (0.038)

math * exp -0.001 -0.001 -0.001 -0.002 -0.002 -0.007*

(0.002) (0.001) (0.001) (0.002) (0.002) (0.004)

verbal score -0.025 0.104*** -0.183*** -0.183*** 0.138*** -0.149***

(0.018) (0.016) (0.016) (0.017) (0.017) (0.045)

verbal * exp 0.006*** 0.007*** 0.001 0.002 0.005*** 0.021***

(0.002) (0.002) (0.002) (0.002) (0.002) (0.004)

mech. score -0.002 -0.066*** 0.177*** 0.160*** -0.081*** 0.189***

(0.016) (0.014) (0.014) (0.015) (0.015) (0.039)

mech * exp -0.000 -0.001 -0.000 0.003 -0.000 0.001

(0.002) (0.001) (0.002) (0.002) (0.002) (0.004)

science score 0.029 -0.007 0.042** 0.073*** -0.019 0.118***

(0.019) (0.016) (0.017) (0.018) (0.017) (0.045)

science * exp -0.003 -0.001 -0.001 0.001 -0.000 -0.005

(0.002) (0.002) (0.002) (0.002) (0.002) (0.005)

interp. skill 0.013 0.027** -0.030*** -0.020 0.050*** 0.039

(0.013) (0.011) (0.011) (0.012) (0.012) (0.031)

interp * exp -0.000 0.001 0.000 0.001* -0.001 0.002

(0.001) (0.001) (0.001) (0.001) (0.001) (0.002)

education 0.096*** 0.172*** -0.083*** 0.003 0.112*** 0.299***

(0.004) (0.004) (0.004) (0.004) (0.004) (0.010)

educ * exp -0.002*** -0.001*** -0.001*** -0.001*** 0.001** -0.005***

(0.000) (0.000) (0.000) (0.000) (0.000) (0.001)

male -0.074*** -0.312*** 0.584*** 0.511*** -0.433*** 0.275***

(0.020) (0.017) (0.016) (0.017) (0.018) (0.048)

male * exp 0.003 0.003 0.000 -0.000 0.007*** 0.013**

(0.002) (0.002) (0.002) (0.002) (0.002) (0.005)

black -0.019 -0.028 -0.057*** -0.058*** 0.009 -0.153***

(0.023) (0.020) (0.019) (0.020) (0.021) (0.056)

black * exp -0.003 -0.006*** 0.006*** 0.006*** -0.006** -0.003

(0.002) (0.002) (0.002) (0.002) (0.002) (0.006)

Hispanic 0.073*** 0.149*** -0.103*** -0.058*** 0.100*** 0.162***

(0.024) (0.021) (0.022) (0.022) (0.022) (0.059)

Hispanic * exp -0.001 -0.002 -0.000 0.002 0.001 0.000

(0.003) (0.002) (0.002) (0.003) (0.002) (0.007)

Constant -1.396*** -2.324*** 0.695*** -0.462*** -1.278*** -4.764***

(0.059) (0.052) (0.051) (0.053) (0.054) (0.141)

Observations 76,060 76,060 76,060 76,060 76,060 76,060

R-squared 0.130 0.345 0.282 0.166 0.232 0.177

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: Sample is restricted to workers with 0 to 25 years of experience who took the ASVAB tests before entering

the labor market. See Appendix B for the O*Net task categories used to create the task measures that are

the dependent variables. The dependent variable in column 6 is the sum of the other five task measures. The

interaction of education and experience is defined as experience times (education minus the mean of education).

Standard errors are clustered at the worker level.

60

Table 7

Experience profiles of each task, with worker fixed effects and task demand measures

(1) (2) (3) (4) (5) (6)

math tasks verbal tasks mechanical tasks science tasks interp. tasks sum of tasks

exp 2 to 3 0.042*** 0.079*** -0.007 0.017** 0.035*** 0.167***

(0.009) (0.007) (0.007) (0.007) (0.008) (0.021)

exp 4 to 6 0.063*** 0.133*** 0.000 0.037*** 0.055*** 0.289***

(0.011) (0.009) (0.009) (0.009) (0.010) (0.028)

exp 7 to 9 0.083*** 0.175*** -0.014 0.050*** 0.089*** 0.383***

(0.015) (0.013) (0.013) (0.013) (0.014) (0.039)

exp 10 to 12 0.071*** 0.196*** -0.026 0.051*** 0.131*** 0.423***

(0.021) (0.017) (0.017) (0.017) (0.018) (0.052)

exp 13 to 15 0.095*** 0.225*** -0.047** 0.063*** 0.169*** 0.503***

(0.027) (0.023) (0.022) (0.022) (0.024) (0.068)

exp 16 to 18 0.125*** 0.245*** -0.049* 0.065** 0.198*** 0.584***

(0.032) (0.027) (0.027) (0.027) (0.028) (0.081)

exp 19 to 21 0.146*** 0.245*** -0.063** 0.044 0.217*** 0.589***

(0.039) (0.032) (0.032) (0.032) (0.034) (0.097)

exp 22 to 25 0.154*** 0.254*** -0.077** 0.051 0.259*** 0.641***

(0.045) (0.037) (0.037) (0.037) (0.039) (0.112)

Constant -0.167*** -0.235*** -0.045*** -0.151*** -0.072*** -0.670***

(0.013) (0.011) (0.011) (0.011) (0.011) (0.032)

Observations 113,080 113,080 113,080 113,080 113,080 113,080

R-squared 0.009 0.035 0.002 0.002 0.019 0.019

Number of id 12,527 12,527 12,527 12,527 12,527 12,527

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: Sample is restricted to workers with 0 to 25 years of experience. All regressions include worker fixed effects.

See Appendix B for the O*Net task categories used to create the task measures that are the dependent variables.

The dependent variable in column 6 is the sum of the other five task measures. The excluded experience category

is 0 to 1 year. All regressions also include a demand index for each task in each year, calculated as the year fixed

effect from a regression in the March CPS of each task on a set of education dummies, gender, race, and a cubic

in potential experience; this regression restricts to workers aged 25 to 45.

61

Table 8

Effects of layoffs on experience paths

(1) (2) (3) (4) (5) (6)

math tasks verbal tasks mech. tasks science tasks interp. tasks sum of tasks

layoff in last yr -0.053*** -0.059*** 0.010 -0.025*** -0.033*** -0.160***

(0.011) (0.009) (0.009) (0.009) (0.010) (0.028)

layoff 2 yrs ago -0.031*** -0.040*** 0.003 -0.017** -0.023** -0.107***

(0.010) (0.009) (0.008) (0.009) (0.009) (0.026)

layoff 3 yrs ago -0.012 -0.008 0.005 -0.012 0.000 -0.027

(0.011) (0.009) (0.009) (0.009) (0.010) (0.028)

layoff 4 yrs ago -0.014 -0.004 0.013 0.001 -0.002 -0.006

(0.012) (0.010) (0.010) (0.010) (0.010) (0.030)

exp 2 to 3 0.038*** 0.076*** -0.008 0.013* 0.033*** 0.151***

(0.010) (0.008) (0.008) (0.008) (0.008) (0.024)

exp 4 to 6 0.062*** 0.126*** -0.002 0.033*** 0.049*** 0.268***

(0.012) (0.010) (0.010) (0.010) (0.011) (0.030)

exp 7 to 9 0.083*** 0.165*** -0.016 0.049*** 0.078*** 0.358***

(0.017) (0.014) (0.013) (0.014) (0.014) (0.041)

exp 10 to 12 0.072*** 0.182*** -0.028 0.051*** 0.115*** 0.393***

(0.022) (0.018) (0.018) (0.018) (0.019) (0.055)

exp 13 to 15 0.095*** 0.206*** -0.044* 0.068*** 0.146*** 0.471***

(0.029) (0.024) (0.023) (0.024) (0.025) (0.071)

exp 16 to 18 0.125*** 0.222*** -0.042 0.078*** 0.165*** 0.549***

(0.035) (0.029) (0.028) (0.029) (0.031) (0.087)

exp 19 to 21 0.147*** 0.221*** -0.056* 0.063* 0.178*** 0.552***

(0.042) (0.035) (0.034) (0.034) (0.036) (0.104)

exp 22 to 25 0.154*** 0.221*** -0.067* 0.072* 0.211*** 0.590***

(0.048) (0.040) (0.039) (0.039) (0.042) (0.119)

Constant -0.152*** -0.204*** -0.057*** -0.145*** -0.046*** -0.605***

(0.013) (0.011) (0.011) (0.011) (0.012) (0.033)

Observations 104,013 104,013 104,013 104,013 104,013 104,013

R-squared 0.007 0.027 0.002 0.001 0.016 0.014

Number of id 12,371 12,371 12,371 12,371 12,371 12,371

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: All regressions include worker fixed effects. See Appendix B for the O*Net task categories used to create

the task measures that are the dependent variables. The dependent variable in column 7 is the sum of the other

five task measures. Tasks are in standard deviations. I classify a job change as a layoff if the worker reports he

left his prior job due to being fired or a plant closing.

62

Table 9

Effects of layoffs on wages

(1) (2) (3)

Log real wage Occ-predicted wage Occ-predicted wage

layoff in last year -0.057*** -0.012*** -0.011***

(0.006) (0.002) (0.002)

layoff 2 years ago -0.043*** -0.008*** -0.008***

(0.006) (0.002) (0.002)

layoff 3 years ago -0.014** -0.003* -0.002

(0.006) (0.002) (0.002)

layoff 4 years ago -0.023*** -0.001 -0.003

(0.007) (0.002) (0.002)

exp 2 to 3 0.105*** 0.016*** 0.017***

(0.005) (0.001) (0.002)

exp 4 to 6 0.189*** 0.033*** 0.034***

(0.007) (0.002) (0.002)

exp 7 to 9 0.249*** 0.045*** 0.046***

(0.009) (0.002) (0.003)

exp 10 to 12 0.269*** 0.049*** 0.051***

(0.012) (0.003) (0.004)

exp 13 to 15 0.288*** 0.054*** 0.058***

(0.016) (0.004) (0.005)

exp 16 to 18 0.287*** 0.059*** 0.064***

(0.020) (0.005) (0.006)

exp 19 to 21 0.271*** 0.057*** 0.063***

(0.023) (0.006) (0.007)

exp 22 to 25 0.271*** 0.056*** 0.062***

(0.027) (0.007) (0.008)

Constant 2.208*** 2.367*** 2.364***

(0.008) (0.002) (0.002)

Observations 103,690 103,312 103,312

R-squared 0.100 0.042 0.043

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: All regressions include worker fixed effects. See Appendix B for

the O*Net task categories used to create the task measures that are the

dependent variables. The dependent variable in column 1 is the log real

wage in 2006 dollars. The dependent variable in column 2 is the predicted

log real wage from a regression of wages on the ASVAB scores, interper-

sonal skill, education, and the five task measures. The dependent variable

in column 3 is the predicted log real wage from a regression of wages on

the ASVAB scores, interpersonal skill, education, the five task measures,

education interacted with all five task measures, and each “own” score

interacted with its task measure. Tasks are in standard deviations. I clas-

sify a job change as a layoff if the worker reports he left his prior job due

to being fired or a plant closing.63

Appendix Tables

Appendix Table 1

Skill and task correlations

Panel A: Skill Measures

Math Verbal Mechanical Science Interpersonal

Math 1.00

Verbal 0.77 1.00

Mechanical 0.63 0.62 1.00

Science 0.74 0.79 0.78 1.00

Interpersonal 0.01 0.03 -0.01 0.01 1.00

Education 0.55 0.50 0.28 0.42 0.03

Panel B: Task Measures

Math Verbal Mechanical Science Interpersonal

Math 1.00

Verbal 0.62 1.00

Mechanical -0.22 -0.54 1.00

Science 0.13 -0.15 0.67 1.00

Interpersonal 0.46 0.77 -0.56 -0.30 1.00

Notes: Math, verbal, mechanical, and science skill are measured by

ASVAB test scores. Interpersonal skill is the answer to a question

of how sociable the worker is, and is only available in the NLSY79.

See Appendix B for the O*Net task categories used to create these

task measures. All skill and task measures are in standard devia-

tions.

64

Appendix Table 2

Correlations between tasks and an occupation earnings measure

Task measure Correlation with Earnings Measure

Math 0.47

Verbal 0.53

Mechanical -0.03

Science 0.29

Interpersonal 0.23

Notes: The occupation earnings measure is the occupation

fixed effect from a regression using the March CPS of log earn-

ings on seven education dummies, gender, race, year fixed ef-

fects, and a quadratic in potential experience. I restrict this

regression to full-time workers aged 35 to 59 from 1980 to 1999.

65

Appendix Table 3

Selected gaps in task content, by experience level

Panel A: Gender gaps (male minus female)

Experience: 0 5 10 20 25

Task:

Math -0.125 -0.098 -0.115 -0.175 -0.160

Verbal -0.440 -0.461 -0.457 -0.535 -0.537

Mechanical 0.810 0.858 0.851 0.871 0.880

Science 0.653 0.728 0.743 0.719 0.731

Interpersonal -0.542 -0.543 -0.524 -0.599 -0.604

Panel B: Race gaps (white minus black)

Experience: 0 5 10 20 25

Task:

Math 0.254 0.276 0.301 0.263 0.257

Verbal 0.305 0.307 0.324 0.287 0.264

Mechanical -0.046 -0.038 -0.019 -0.063 -0.084

Science 0.141 0.182 0.170 0.107 0.100

Interpersonal 0.173 0.201 0.200 0.196 0.202

Panel C: Education gaps (≥16 minus ≤12)

Experience: 0 5 10 20 25

Task:

Math 0.712 0.723 0.742 0.741 0.681

Verbal 1.175 1.179 1.158 1.081 1.049

Mechanical -0.762 -0.774 -0.715 -0.708 -0.595

Science -0.007 -0.008 0.012 -0.082 -0.023

Interpersonal 0.872 0.896 0.850 0.782 0.739

Notes: Tasks are in standard deviations. These gaps are

produced by estimating career paths separately by gen-

der, race, and education level with worker fixed effects,

treating the mean of the fixed effects as the intercept

term.

66

Appendix Table 4

Experience profiles of math tasks, by percentile

Panel A: Education 12 and under

(1) (2) (3) (4) (5)

Percentile 99th 90th 50th 10th 1st

exp 0.018*** 0.014*** 0.015*** 0.014*** 0.000

(0.000) (0.000) (0.000) (0.000) (0.000)

Constant 1.643*** 0.671*** -0.396*** -1.520*** -2.673

(0.001) (0.001) (0.000) (0.001) (0.000)

Panel B: Education 16 and over

(1) (2) (3) (4) (5)

Percentile 99th 90th 50th 10th 1st

exp -0.004*** -0.006*** 0.012*** 0.009*** 0.016***

(0.000) (0.000) (0.000) (0.000) (0.001)

Constant 2.423*** 1.609*** 0.147*** -0.968*** -2.349***

(0.003) (0.002) (0.002) (0.003) (0.007)

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: See Appendix B for the O*Net task categories used to create

the task measures that are the dependent variables. Tasks are in stan-

dard deviations. The dependent variables are the percentile values of

math tasks at each experience level for each education group.

67

Appendix Table 5

Experience profiles of each task, with worker fixed effects (and no task demand measures)

(1) (2) (3) (4) (5) (6)

math tasks verbal tasks mechanical tasks science tasks interp. tasks sum of tasks

exp 2 to 3 0.053*** 0.095*** -0.013** 0.010 0.045*** 0.190***

(0.008) (0.006) (0.006) (0.006) (0.007) (0.019)

exp 4 to 6 0.088*** 0.169*** -0.012** 0.024*** 0.077*** 0.346***

(0.007) (0.006) (0.006) (0.006) (0.006) (0.018)

exp 7 to 9 0.120*** 0.234*** -0.031*** 0.034*** 0.123*** 0.479***

(0.008) (0.007) (0.007) (0.007) (0.007) (0.020)

exp 10 to 12 0.115*** 0.274*** -0.044*** 0.038*** 0.175*** 0.558***

(0.009) (0.008) (0.008) (0.008) (0.008) (0.024)

exp 13 to 15 0.145*** 0.315*** -0.061*** 0.062*** 0.218*** 0.679***

(0.011) (0.009) (0.009) (0.009) (0.010) (0.028)

exp 16 to 18 0.201*** 0.362*** -0.067*** 0.069*** 0.262*** 0.827***

(0.012) (0.010) (0.010) (0.010) (0.011) (0.030)

exp 19 to 21 0.245*** 0.392*** -0.089*** 0.036*** 0.296*** 0.879***

(0.012) (0.010) (0.010) (0.010) (0.011) (0.031)

exp 22 to 25 0.270*** 0.423*** -0.111*** 0.012 0.346*** 0.940***

(0.012) (0.010) (0.010) (0.010) (0.010) (0.029)

Constant -0.196*** -0.281*** -0.035*** -0.142*** -0.097*** -0.751***

(0.005) (0.005) (0.004) (0.004) (0.005) (0.014)

Observations 113,080 113,080 113,080 113,080 113,080 113,080

R-squared 0.008 0.034 0.002 0.001 0.019 0.019

Number of id 12,527 12,527 12,527 12,527 12,527 12,527

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: Sample is restricted to workers with 0 to 25 years of experience. All regressions include worker fixed effects.

See Appendix B for the O*Net task categories used to create the task measures that are the dependent variables.

The dependent variable in column 6 is the sum of the other five task measures. The excluded experience category is

0 to 1 year.

68

Appendix Table 6

Early-career experience paths, by survey

Panel A: NLSY79

(1) (2) (3) (4) (5)

math tasks verbal tasks mechanical tasks science tasks interp. tasks

exp 2 to 3 0.066*** 0.093*** -0.013 0.024** 0.041***

(0.011) (0.009) (0.009) (0.009) (0.009)

exp 4 to 6 0.093*** 0.164*** -0.020** 0.041*** 0.071***

(0.010) (0.008) (0.009) (0.009) (0.009)

Constant -0.166*** -0.211*** -0.030*** -0.130*** -0.093***

(0.007) (0.006) (0.006) (0.006) (0.006)

Panel B: NLSY97

(1) (2) (3) (4) (5)

math tasks verbal tasks mechanical tasks science tasks interp. tasks

exp 2 to 3 0.037*** 0.092*** -0.011 -0.001 0.044***

(0.011) (0.008) (0.008) (0.008) (0.009)

exp 4 to 6 0.086*** 0.175*** -0.001 0.008 0.081***

(0.010) (0.008) (0.008) (0.008) (0.009)

Constant -0.198*** -0.289*** -0.142*** -0.210*** -0.001

(0.007) (0.006) (0.006) (0.005) (0.006)

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Notes: Sample is restricted to workers with 0 to 6 years of experience. All regressions

include worker fixed effects. See Appendix B for the O*Net task categories used to create

the task measures that are the dependent variables. The dependent variable in column

6 is the sum of the other five task measures. The top panel only includes NLSY79

respondents, while the bottom panel only includes NLSY97 respondents. The excluded

experience category is 0 to 1 year.

69

Appendix Table 7

Moves to management: changes in tasks

Panel A: Education 12 and under

math tasks verbal tasks mech. tasks science tasks interp. tasks

Prior to manager: 0.24 0.27 -0.18 -0.02 0.89

As manager: 0.53 0.75 -0.36 0.06 0.89

Difference: 0.29 0.48 -0.18 0.08 0.45

As % of 25-year increase: 90.6 126.3 360.0 100.0 150.0

Panel B: Education 13 to 15

math tasks verbal tasks mech. tasks science tasks interp. tasks

Prior to manager: 0.43 0.55 -0.47 -0.15 0.66

As manager: 0.64 0.88 -0.58 -0.09 0.93

Difference: 0.21 0.33 -0.11 0.06 0.27

As % of 25-year increase: 100.0 73.3 68.8 -333.3 81.8

Panel C: Education 16 and over

math tasks verbal tasks mech. tasks science tasks interp. tasks

Prior to manager: 0.74 0.84 -0.75 -0.24 0.73

As manager: 0.84 1.01 -0.79 -0.24 0.73

Difference: 0.1 0.17 -0.04 0 0.16

As % of 25-year increase: 111.1 58.6 30.8 0.0 48.5

Notes: See Appendix B for the O*Net task categories used to create the task measures that are

the dependent variables. Tasks are in standard deviations. I measure the tasks in the year of and

year prior to an observation in a management or supervisory occupation. The 25-year increase

figures are taken from fixed-effect regressions of each task on a set of experience category dummies,

separately for each group. These regressions do not include the task demand measures.

70

Appendix Table 8

Summary statistics for expanded sample

NLSY79 NLSY97

Mean Stdev Mean Stdev

Male 0.52 0.50 0.52 0.50

Black 0.25 0.43 0.25 0.43

Hispanic 0.16 0.36 0.20 0.40

Education 13.36 2.26 12.79 2.49

Experience 10.38 8.06 3.84 2.97

Math score 0.05 0.99 -0.04 0.92

Verbal score 0.05 0.97 -0.05 0.92

Mechanical score 0.09 1.00 0.00 0.88

Science score 0.06 0.99 -0.02 0.92

Interpersonal skill 0.00 0.98 – –

Math tasks -0.05 0.98 -0.16 0.99

Verbal tasks -0.01 0.98 -0.21 0.95

Mechanical tasks -0.05 0.98 -0.12 0.94

Science tasks -0.08 0.94 -0.20 0.86

Interpersonal tasks 0.03 0.98 0.03 0.93

Total observations 75,069 35,732

Number of ID 6,249 5,505

Notes: The sample includes workers who transitioned

to the labor market in 1978 or later. It therefore

includes those who took the ASVAB after entering the

labor market. This sample is used to estimate average

career paths and the effects of layoffs on occupations

and wages. Experience is years since the transition

began. The task measures refer to the current or most

recent job.

71

Appendix A: A Simple Model of Wage Determination

An occupation γ is a vector of tasks (j,k). A worker i is a vector of skills (sij,sik,sig).

The terms sij and sik denote specific skills, useful in performing tasks j and k

respectively, while sig denotes general skill.

There are Γ occupations, indexed by γ (each a different bundle (jγ,kγ)). The amount

xiγ of output produced by worker i in occupation γ is

xiγ = f(sij, sik, sig; jγ, kγ).

The function f relates a worker’s skills and the tasks required in the occupation to the

amount of product produced by the worker in that occupation. I assume that this

function has two key features. First, the specific skills make a worker more productive

in their associated tasks – sj for j and sk for k. Second, general skill sg makes a worker

more productive in performing both tasks.

Demand for Tasks

Demand for output comes from outside the model. The price of occupation γ’s output

xγ is

Pxγ = h(jγ, kγ).

The costs of creating a position in occupation γ as well as the occupation output, given

worker skill, depend only on (or are at least approximated by) a function of the

occupation task requirements j and k, so the price of an occupation’s output depends

on only j and k. That is, there is a mapping from the task content of an occupation to

the price of the occupation’s output.

Determination of Wages in Occupation γ

The labor market is competitive, with spot markets and no long-term contracting. The

wage of worker i in occupation γ is equal to his marginal revenue product, which is

72

wiγ = Pxγf(sij, sik, sig; jγ, kγ).

This is the price of the output times the amount produced by the worker. The log wage

of worker i in occupation γ is

lnwiγ = lnPxγ + ln(f(sij, sik, sig; jγ, kγ)).

The wage function is an equilibrium condition that reflects the demand for output t and

the production function relating tasks j and k and the worker’s skills to output.

Occupation choice of worker i

A worker chooses an occupation γ – a pair (j,k) – to maximize his wage. Let his

optimal occupation be γ∗ and the associated j and k be

j∗γ = j∗γ(sij, sik, sig; β1)

k∗γ = k∗γ(sij, sik, sig; β2)

The task choices are a function of the workers’ skills and the β terms, which represent

demand for each task.

Let lnPxγ∗ = Π(j∗γ∗(sij, sik, sig; β1), k∗γ∗(sij, sik, sig; β2)). In equilibrium, then, wages for

worker i in his optimal occupation are

lnw∗i = Π(j∗γ∗(sij, sik, sig; β1), k∗γ∗(sij, sik, sig; β2))+ln f(sij, sik, sig; j

∗γ∗(sij, sik, sig; β1), k∗γ∗(sij, sik, sig; β2))

Therefore, wages in equilibrium are a function of the worker’s skills and demand

conditions for each type of task j and k.

An example

73

Suppose that the log of the production function f is

ν1j − ν2j2 + ν3k − ν4k

2 + ν5sjj + ν6skk + ν7sgj + ν8sgk

This displays the two key properties discussed above. Performance of task j is more

productive if the worker has higher skills sj and sg, and performance of task k is more

productive if the worker has higher skills sk and sg. Skills here are not useful on their

own (i.e., when they are not used to perform a task), so there are no separate terms for

the skills. Production when skills are equal to zero should be thought of as production

of the average worker, and the skill terms as deviations form the average.

Also suppose that the price of an occupation’s output can be written as

Π(j∗(sij, sik, sig; β1), k∗(sij, sik, sig; β2)) = π1jγ − π2j2γ + π3kγ − π4k

2γ + π5jγkγ.

The π5 term can be either positive or negative, depending on the distribution of

demand across occupations. With these formulations, then the log wage function for

worker i in occupation γ which uses task levels jγ and kγ is

ln(wiγ) = α1jγ − α2j2γ + α3sijjγ + α4kγ − α5k

2γ + α6sikkγ + α7sigjγ + α8sigkγ + α9jγkγ.

This is the wage function given in the model of Section 2. The coefficients come from

the combination of the production function and the demand for output. For example,

α1 = π1 + ν1. This also clarifies how a change in demand for output can affect a

worker’s choice of occupation tasks. If demand for output rises in occupations that use

high levels of j, then we can think of this as an increase in π1, which leads to an increase

in α1. This will induce a worker to enter a higher-j occupation, all else being equal.

To be clear, many different wage functions could result from this model setup given

different specifications of production functions and demand for output. This is merely

one example.

74

Appendix B: O*Net Task Measures and Descriptions

Math Tasks

Mathematics knowledge: Knowledge of arithmetic, algebra, geometry, calculus,

statistics, and their applications.

Mathematics skill: Using mathematics to solve problems.

Analyzing data or information: Identifying the underlying principles, reasons, or

facts of information by breaking down information or data into separate parts.

Mathematical reasoning ability: The ability to choose the right mathematical

methods or formulas to solve a problem.

Number facility ability: The ability to add, subtract, multiply, or divide quickly and

correctly.

Verbal Tasks

Reading comprehension: Understanding written sentences and paragraphs in

work-related documents.

Writing skill: Communicating effectively in writing as appropriate for the needs of the

audience.

English language knowledge: Knowledge of the structure and content of the English

language including the meaning and spelling of words, rules of composition, and

grammar.

Written expression ability: The ability to communicate information and ideas in

writing so others will understand.

Mechanical Tasks

Handling and moving objects: Using hands and arms in handling, installing,

positioning, and moving materials, and manipulating things.

Inspecting equipment, structures, or material: Inspecting equipment, structures,

or materials to identify the cause of errors or other problems or defects.

Controlling machines and processes: Using either control mechanisms or direct

physical activity to operate machines or processes (not including computers or vehicles).

75

Operating Vehicles, Mechanized Devices, or Equipment: Running,

maneuvering, navigating, or driving vehicles or mechanized equipment, such as forklifts,

passenger vehicles, aircraft, or water craft.

Repairing and maintaining mechanical equipment: Servicing, repairing,

adjusting, and testing machines, devices, moving parts, and equipment that operate

primarily on the basis of mechanical (not electronic) principles.

Repairing and maintaining electrical equipment: Servicing, repairing,

calibrating, regulating, fine-tuning, or testing machines, devices, and equipment that

operate primarily on the basis of electrical or electronic (not mechanical) principles.

Equipment maintenance skill: Performing routine maintenance on equipment and

determining when and what kind of maintenance is needed

Mechanical knowledge: knowledge of machines and tools, including their designs,

uses, repair, and maintenance

Science Tasks

Science skill: Using scientific rules and methods to solve problems.

Engineering and technology knowledge: Knowledge of the practical application of

engineering science and technology. This includes applying principles, techniques,

procedures, and equipment to the design and production of various goods and services.

Biology knowledge: Knowledge of plant and animal organisms, their tissues, cells,

functions, interdependencies, and interactions with each other and the environment.

Chemistry knowledge: Knowledge of the chemical composition, structure, and

properties of substances and of the chemical processes and transformations that they

undergo. This includes uses of chemicals and their interactions, danger signs,

production techniques, and disposal methods.

Physics knowledge: Knowledge and prediction of physical principles, laws, their

interrelationships, and applications to understanding fluid, material, and atmospheric

dynamics, and mechanical, electrical, atomic and sub- atomic structures and processes.

Interpersonal Tasks

76

Establishing and maintaining interpersonal relationships: Developing

constructive and cooperative working relationships with others, and maintaining them

over time.

Resolving conflicts and negotiating with others: Handling complaints, settling

disputes, and resolving grievances and conflicts, or otherwise negotiating with others.

Customer and personal service: Knowledge of principles and processes for

providing customer and personal services. This includes customer needs assessment,

meeting quality standards for services, and evaluation of customer satisfaction.

Active listening: Giving full attention to what other people are saying, taking time to

understand the points being made, asking questions as appropriate, and not

interrupting at inappropriate times.

77

Appendix C: A Model of College Attendance and College Major

The education decision

In the static occupational choice model, I took a worker’s skill vector as given. Now, I

allow a worker to invest in his skills prior to entering the labor market by attending

college.

From the wage function laid out in section 2.1, one can show that higher skills have a

positive wage return in the labor market. Specifically, ∂w∂sj

> 0, ∂w∂sk

> 0, and ∂w∂sg

> 0

(where w denotes the log wage). While the solutions for these terms are not simple, it is

easy to see that they must be positive. If the worker sees an increase in any of the three

skills and simply holds his j and k constant, then his wage increases due to the

multiplicative skill-task terms in the wage function.63 If the worker can increase his

wage by staying in his current occupation, then it is clear that his wage will also

increase in his new choice of occupation.

Because of the return to skills, the worker is willing to pay a cost to invest in his skills

prior to entering the labor market. I now add a stage of the model prior to labor market

entry in which the worker decides whether or not to attend college. The worker finishes

high school and observes his skill endowments sj0, sk0, and sg0. He may enter the labor

market and earn the wages associated with those skills, or he make a small skill

investment (i.e., attend a 2-year college) or a large skill investment (a 4-year college).

A worker who decides to attend college is investing in general skill sg, and then may

choose either sj or sk to invest in as well; this is done through his choice of major. If

the worker goes to 2-year college, which has tuition cost c1, his skills grow as follows:

63Recall that j and k are assumed to always be positive.

78

sg = (1 + µ1)sg0

sf = (1 + µ1)sf0

where µ1 > 0 and field f can be either j or k. General skill grows, perhaps from “core”

classes, and one specific skill grows from the student’s choice of major. If he chooses the

4-year degree, which costs c2 > c1, his skills are:

sg = (1 + µ2)sg0

sf = (1 + µ2)sf0

where µ2 > µ1. A 4-year college is both more expensive and a more productive

investment in skills, both general and specific. The skill gained from college is thus just

a function of the test scores.

As an additional option, a worker may undertake a joint 4-year degree in which he

studies both j and k (that is, he gets a boost in general skill and both specific skills).

This comes with a cost c3 > c2, which reflects the psychic cost of taking extra courses or

increased difficulty, in addition to any monetary cost. An example of this type of degree

might be an engineering program, which is high in math, mechanical, and science

content.

Who will go to college?

In what follows, for simplicity, I ignore the boost in general skill sg from attending

college and focus only on sj and sk. I also assume that workers do not discount the

future, although this is not important for the analysis. I also abstract from skill

accumulation of specific skills after labor market entry (essentially, I just consider a

repeated version of the static occupation choice model). Let us assume that a worker

79

has 40 periods of potential work. If he goes to 2-year college, he will work the following

38 periods. The worker prefers a 2-year degree in k to no college if

38[w(sj, (1 + µ1)sk)]− 40w(sj, sk)− c1 > 0

which is approximately equivalent to

38µ1sk[∂w

∂sk]− 2w(sj, sk)− c1 > 0.

Clearly attendance is increasing in µ1 and decreasing in c1. What about sk? Both the

benefit of college and the opportunity cost are increasing in sk, so the solution is not

obvious. Let the left-hand side of the above be denoted by P2k. Then

∂P2k

∂sk= 38µ1sk[

∂2w

∂s2k

] + 38µ1[∂w

∂sk]− 2[

∂w

∂sk].

Now I refer back to the wage function in the previous section. I showed there that

∂w∂sk

> 0, although the solution is not elegant. Furthermore, one can show that

∂2w

∂s2k

=2α2

6α2

4α2α5 − α29

> 0.

From the above, it is clear that the probability of attending college of any kind will be

increasing in sk (and the other skills) as long as µ1 is large enough. If µ1 is very low,

higher-skilled workers find the opportunity cost too high to attend. 64 A result in which

college attendance was not increasing in skill would be difficult to believe, suggesting

that µ1 is indeed large enough.

64If the worker discounts the future, then the required value of µ1 rises, because the 38 periods of workare discounted more than the 2 periods of opportunity cost.

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Similarly, one can show that attendance of 4-year college relative to 2-year college is

also increasing in sk, sj, and sg if (µ2 − µ1) is large enough.

What will they study?

Now, what will a college attendee study? Using the same techniques, it is easy to show

that a worker attending 2-year college prefers to study subject j instead of k if

sj(∂w

∂sj) > sk(

∂w

∂sk)

sj > sk(∂w∂sk∂w∂sj

).

If the two skills have equal marginal returns, then the worker simply chooses to study in

his stronger field. However, consider the case in which task k has a lower market return

than task j (α4 < α1). Then it is also true that ∂w∂sk

< ∂w∂sj

. In this case, a worker with

equal skills sj and sk will choose to study j, the more lucrative field. To study k

instead, he will require his sk to be larger than sj, where the size of the gap is

determined by the ratio of the two derivatives.

The worker also has the option of a joint degree, in which he studies both j and k at

the 4-year level. The worker’s decision here is similar to his decision to attend or not

attend, except that now he must prefer the joint 4-year degree to both a 4-year degree

in j and a 4-year degree in k, assuming he already prefers a 4-year degree of some sort.

Therefore, both of the following two conditions must hold:

36[w((1 + µ2sj), (1 + µ2)sk)]− 40w((1 + µ2)sj, sk)− (c3 − c2) > 0

36[w((1 + µ2sj), (1 + µ2)sk)]− 40w(sj, (1 + µ2)sk)− (c3 − c2) > 0,

which is approximately equivalent to these two conditions:

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36µ2sk[∂w

∂sk]− 4w((1 + µ2)sj, sk)− (c3 − c2) > 0

36µ2sk[∂w

∂sj]− 4w(sj, (1 + µ2)sk)− (c3 − c2) > 0.

It is not difficult to see that meeting these two conditions requires both sj and sk to be

large, since the first condition is increasing in sk and the second increasing in sj, given

the same qualifications about the size of µ2. Workers pursuing a joint degree, then, are

workers with high values of both skills. If they have a high value of one skill but not the

other, they will be found in a regular 4-year degree program in their dominant skill.

Finally, I consider the effect of the substitutability or complementarity of tasks on this

result. It is intuitive that both ∂w∂sj

and ∂w∂sk

are increasing in α9; that is, when the two

tasks are complements, the marginal return to each skill is higher, because a rise in one

skill raises both tasks. From the conditions for preferring a joint 4-year degree, it is

clear that a higher value of α9 makes the probability of pursuing a joint degree higher.

Workers will be more likely to jointly study two subjects that are complementary rather

than two subjects that are substitutes.

Using education as a measure of general skill

College attendance is assumed to bring a boost in general skill and in one specific skill.

It is thus not purely a measure of general skill. However, unless college attendees

overwhelmingly study one set of subjects instead of other subjects, then on balance,

education mostly carries information about general skill. Furthermore, in a separate

analysis, I find that the ASVAB scores are strong predictors of what workers will study

in college; those with high math scores study math-related subjects, and so on. This

implies that information about the specific content of college (i.e., majors) is carried at

least partially by the ASVAB scores. By controlling for those scores, the effect of

education is primary as a measure of general skill.

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