Abstract
This paper develops a new empirical framework for analyzing occupational choice and career progression. I merge the NLSYs with O*Net and find that pre-market skills (primarily ASVAB test scores) predict the task content of the workers’ occupations. These measures account for 71 percent of the gender gap in science and engineering occupations. Career trajectories are similar across workers, so that initial differences in occupation persist over time. I then quantify the effect of layoffs on career trajectory and find that a layoff erases one-fourth of a worker’s total career increase in task content but this effect only lasts two years.
I. 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? I address these two questions with a particular focus on gender gaps in occupational outcomes.
This paper develops a new framework for analyzing occupational choice and career progression, focusing on the role of pre-labor market skills in determining career outcomes. I develop a simple model that 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 remarkably similar across workers, meaning that initial gaps in occupation persist almost perfectly over the course of a career. Pre-market skills are important 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 National Longitudinal Surveys of Youth,) with data on the task requirements of their occupations (O*Net). The NLSYs provide me with a set of pre-market skill measures (the Armed Services Vocational Aptitude Battery test scores) for a panel of individuals whose careers I can see unfold over several decades. The O*Net data allow 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 (math, for example) 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 innate 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.
This paper has two key sets of findings, both of which have important applications to gender gaps in occupation. First, I find that pre-market skills, as measured by the ASVAB component scores (math, verbal, mechanical, and scientific aptitude) and an interpersonal skill measure, predict the task content of the workers’ initial occupations. 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. Skills are multidimensional, and the dimensions matter.
I use this framework to study the differing occupational 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 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 much higher on the mechanical and science tests, particularly at the top of these distributions. Differences in ASVAB scores account for about 10–30 percent of overall occupational gender gaps, including 71 percent of the gender gap in science and engineering occupations. Using only the Armed Forces Qualifying Test (AFQT) score, a commonly used composite of the math and verbal ASVAB components, accounts for virtually none of these gaps.
Second, having established the links between skills and initial occupation choice, I show that career trajectories are similar across worker skill types, implying that initial differences in occupation (including those by race and gender) persist almost perfectly over the course of a career. Sorting into occupations on the skills that I observe happens very quickly; it does not appear that workers are unsure about their suitability for different types of occupations. Pre-market skills have persistent effects on occupational outcomes.
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 (Jacobson, LaLonde, and Sullivan 1993) 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 occupation task content. However, that effect is short-lived. After two 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 primary mechanism driving these wage effects. The effect of a layoff on occupation can account for only about 20 percent of the overall effect on wages.
While the NLSYs (especially the NLSY79) have 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 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, particularly the gender gaps.1
The study of occupational choice has a rich history in economics, and economists have long recognized skills as an important determinant of these choices. Roy (1951) develops a model in which workers have two skills, and comparative advantage and the returns to skills determine which sector the worker enters. Heckman and Sedlacek (1985) present a model that allows for multiple skills, both observed and unobserved, which have varying usefulness in different jobs.2 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 multidimensional 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 (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 et al. 2005; Papageorgiou 2014; James 2013); as employers learning which workers are worthy of promotions (Jovanovic and Nyarko 1996); or as evidence of skill accumulation (Rosen 1972, Sanders 2014).
I contribute to the occupational choice and mobility literatures by developing a framework linking pre-market skills to occupation choices over the course of a career, and by combining data sources to quantify these relationships. 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 average career paths given worker characteristics, which will aid other researchers in interpreting 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 interpreting occupational mobility patterns by examining the relationships between occupations (Poletaev and Robinson 2008; Gathmann and Schönberg 2010). This literature draws on new data sources which allow researchers to look inside the “black box” of census occupation codes and descriptions (Yamaguchi 2010, 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.3 By combining occupation task data with data on a variety of pre-market skill measures, I provide new evidence on this topic.
While the occupation task literature provides an interpretation for individual occupational changes, a framework for interpreting a worker’s entire career remains elusive. A recent paper by Sanders (2014) 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 on later outcomes. A series of papers by Heckman, including Heckman, Stixrud, and Urzua (2006), has shown that both cognitive and noncognitive 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 quantifying 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. Using a wide array of skill measures is particularly important for understanding gender gaps in occupation.
The paper proceeds as follows. Section II presents a model of occupational choice and the determinants of career progression, which will motivate the empirical analysis. Section III describes the data sources, and Section IV describes the empirical strategy. Sections V and VI present the results, which include applications of the occupation choice and career path framework. Section VII concludes.
II. A Model of Occupational Choice
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 characterize 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.
I will not estimate this model but it will help motivate the data construction and empirical analysis, which are the chief contributions of this paper.
A. A One-Period Model of Occupational Choice
An occupation is characterized by a bundle of tasks, which are the technology of production 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 talents, abilities, and knowledge useful for performing tasks. Skills may be specific or general. A specific skill is only useful in performing a given task; an example is knowledge of how to operate a hand saw. A general skill is useful in performing any task. An example of a general skill is problem-solving ability, which makes a worker more productive in whatever task he is performing.
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.4 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 1, I provide a simple model of wage determination, based on Altonji and Rosenzweig (2007).5 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 (say, math and interpersonal activities), is
(1)The production function f has two key features. First, higher levels of each specific skill make 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 1), the following flexible log wage formulation results for worker i in an occupation γ that uses task levels jγ and kγ:
(2)I suppress the i and γ subscripts going forward. The wage coefficients reflect a combination 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.6
The first two terms show diminishing returns and increasing costs of fielding an occupation 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 but 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.7 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.8
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 that 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 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.9
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.10
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
(3)
(4)which, after solving and substituting, lead to solutions of
(5)
(6)The solutions provide information about the relationships between each skill and its “own” task, each skill and the other task, and general skill and each task.11 I discuss each of these relationships separately.
2. Sorting: skills to tasks
First, the relationship between each specific skill and its associated task is positive:
(7)
(8)Second, the relationship of a specific skill with the other task depends on whether the two tasks are substitutes or complements. Specifically,
(9)
(10)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.
Third, the relationship between general skill sg and each task is ambiguous. The derivatives are
(11)
(12)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. 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.
B. 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:
(13)
(14)
(15)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.12
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 elegant. However, the same basic relationships between the skills and tasks hold as in the one-period problem.
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 also could 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
C. Summary of Empirical Implications
The model is meant only to motivate the data construction and empirical analysis. The model suggests two key things to investigate empirically: (1) the relationship of a worker’s skill vector to his choice of occupation task vector, and (2) the persistence of any initial occupation gaps over the course of workers’ careers. In both cases, I am interested in the sign and size of relationships but not in estimating the parameters of the model.
I also will investigate two other issues which play no role in the model. First, I am particularly interested in the role that race and gender play in occupational outcomes, and how those roles interact with the roles of pre-market skills. Second, after I analyze the persistence of occupation gaps by studying career progression, I will look at the effects of a career disruption by analyzing the effect of layoffs on career occupation paths.
III. Data
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 NLSYs for the worker information and O*Net for the occupation information.
A. 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 NLSYs are ideal for this project for two reasons. The first reason is their 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.15
The second key advantage of the NLSYs is the inclusion of the Armed Services Vocational Aptitude Battery (ASVAB) tests, which were taken by NLSY79 respondents in 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 comprehension, 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.16
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.17 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 components 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.18 Studies from within the military have shown that the relevant ASVAB score categories predict performance in their associated military occupations (Sims and Hiatt 2001; Welsh, Kucinkas, and Curran 1990).
I use the ASVAB scores to analyze the sorting patterns of civilian workers into occupations. Given the military’s use of these tests, this is a natural use of the data in the NLSYs. Each military branch combines the scores in different ways to assign workers to occupations so I create my own four composite categories: math, verbal, mechanical, 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.19,20
I also utilize two “noncognitive” skill scores as measures of interpersonal skill. The interpersonal skill score is the average of the Rotter Locus of Control score and the Rosenberg Self-Esteem score.21 The Rotter Locus of Control score measures the degree of control that respondents feel they have over their own lives. The Rosenberg Self- Esteem score measures the respondent’s perceived self-worth. These measures have been used in previous studies of noncognitive skills, including Heckman, Stixrud, and Urzua (2006).22
This gives me a five-dimensional specific skill vector: math, verbal, mechanical, science, and interpersonal skills. I will use years of education as my primary measure of general skill.23 Panel A of Table A1 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 being employed in the first of those two years. I define experience as years since the transition to the labor market began.24 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. A small number of respondents without valid ASVAB scores or interpersonal skill scores are dropped. I also drop the military subsample of the NLSY79.
I use labor market data from 1982 to 2010 in the NLSY79 and from 200zero to two010 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, education, and test scores on average. On the other hand, restricting to those whose ASVAB scores are pre-market skills produces a relatively high-skill sample in the NLSY79. 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).
Summary Statistics
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. 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 pretest 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 dashed vertical lines denote the mean for each group.)25 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 score differences can account for much of the black/white wage gap.
Test Score Densities by Gender
Test Score Densities by Race/Ethnicity
There are also ASVAB score differences by gender, as seen in Figure 1. The math scores are similar for men and women while women score higher than men in verbal. Altonji and Blank (1999) and others have noted that controlling for AFQT cannot explain much of the wage gap between men and women.26 However, men score significantly higher on the mechanical and science components of the ASVAB, particularly at the top of the score distribution.
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, perhaps due to the biases of their teachers, which could lead to test score gaps in teenage years. Fryer and Levitt (2010), for instance, show that gender gaps in math scores in the United States open up only after students have started school.
Educational choices and experiences likely matter as well. Brown and Corcoran (1997) and Altonji (1995) show that boys and girls take different types of high school courses in the United States, 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. Other factors, such as the gender of the instructor in certain courses, also may influence the achievement of boys and girls differentially (Dee 2007; Carrell, Page, and West 2010; Hoffmann and Oreopoulos 2009).
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, males are more likely to study science in college than females; 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 percent 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 precollege-age factors. This does not rule out educational investments differing by gender but it suggests that these investments must be occurring before college. All results in this paper are similar when restricting to this age-restricted sample.
B. 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. Following other researchers who have used these data, I call these measures “tasks” (Autor and Handel 2013).
A total of 159 tasks are rated for each occupation.27 It is useful for my purposes to summarize the data by a smaller number of factors. I require occupation-level28 measures of math, verbal, mechanical, science, and interpersonal tasks to match the worker skill data from the NLSYs. I choose a set of tasks for each category (based on their descriptions given by O*Net), and for each set of tasks, I take the average as my measure for that category.29,30 Results are almost identical when using factor analysis to extract a single factor from each set of tasks instead. I use the simple average method to be consistent with my test score measures. 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 O*Net descriptions are in Appendix 2.
I standardize my five composite task measures to be mean zero and variance one, 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.31 The first five occupations listed are the highest-scoring in each category: mathematicians for math, writers and authors for verbal, and so on.
Task Measures for Selected Occupations, in Standard Deviation Units
Table A2 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.32 Math, verbal, science, and interpersonal tasks are positively correlated with the occupational earnings measure while mechanical tasks are uncorrelated with occupational earnings.
Panel B of Table A1 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 positively correlated in occupations.
IV. Empirical Strategy
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.33 The regression equation is
(16)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), education (a measure of general skill) is measured in years, 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.
I estimate these regressions on workers with experience from zero to two years, to estimate the impact of pre-market skills on early-career occupations,34 and 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 experience, I 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, race, gender, the test scores, education, and interactions between experience and all measures.35 The regression equation is
(17)where Xi is a vector of race, gender, and ability variables, including education and the ASVAB scores (so, in terms of the model, Xi includes the skills sj, sk, and sg). Gender and race are included in Xi because, as I show in the following results, these factors influence initial occupation outcomes as well. 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 from that regression is my measure of demand for that task in that year. I include the demand measure for all five tasks in regression Equation 17 because changing demand for one task may also affect the choices of other tasks.
V. 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 deviation increase in the math ASVAB score leads to a 0.176 standard deviation rise in math task content in the occupation. The other score-task relationships are similar in magnitude, except for mechanical, which is larger (0.288). The interpersonal skill measure’s effect on interpersonal tasks is also positive and significant, though smaller in magnitude than the other relationships.36
Early-Career Occupational Choice Regressions
Second, education (general skill) is positively related to math, verbal, science, and interpersonal tasks, and negatively related to mechanical tasks. This could be because the usefulness of general skill in performing mechanical tasks is low(as in the model), or because education is positively related to omitted variables (say, intelligence) that predict going into certain types of jobs and not others. Overall, one year of education is associated with 0.349 higher total tasks. I will refer back to this number as a benchmark for quantifying career progression later.
Third, the relationships between skills and other tasks vary and are sometimes inconsistent. Math scores positively predict verbal tasks, for example but verbal scores do not positively predict math tasks. Meanwhile, mechanical and science scores each predict the other task positively, as do math and science scores. These results show that in considering occupational outcomes, it is important to include the entire skill vector and not just the own skill.37
Table A3 repeats the analysis of Table 3 but includes a “knot” in the middle of the distribution for each test score. These results show that positive sorting generally occurs throughout the distribution of skills but it is typically strongest in the top of each skill distribution. For instance, the mechanical-to-mechanical relationship is twice as strong in the top half of the mechanical skill distribution than in the bottom half. The math-to-math relationship is strong in the top half of the distribution but small and insignificant in the bottom half.
A. Race and Gender Gaps in Occupation Outcomes
The results of Table 3 help us understand 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.38
Tables 4a and 4b first show the results of regressions of each task on education and dummies for male, black, and Hispanic, with no ASVAB scores (but with year fixed effects), again restricting only to the early years of the career and using the same sample criteria and clustering of standard errors at the worker level as in Table 3. There are substantial race and gender gaps in most of the tasks. Females’ occupations are higher in verbal and interpersonal content while males’ occupations require much more science and mechanical tasks. Relative to whites, blacks are found in occupations that require less of all types of tasks. The race and gender gaps in tasks are large; the male advantage in mechanical and science tasks is equivalent to more than two standard deviations of test scores, using the coefficients from Table 3.
Race and Gender Gaps in Occupation Content
Race and Gender Gaps in Occupation Content
Can ASVAB scores account for 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 substantial; men score 0.51 and 0.33 standard deviations higher than women in mechanical and science, respectively. These differences are especially large at the top of the distribution. About 15 percent 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 percent level) and men scoring 0.03 standard deviations higher in math (significant at the 10 percent level). The math and verbal differences largely even out to leave only small gender differences in AFQT.39
Recall also that Figure 2 plots the densities of each test score for whites, blacks, and Hispanics. 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. A large portion of the black-white gap is explained by including the AFQT score. This is consistent with wage results in Neal and Johnson (1996). However, adding AFQT does little to account for the 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 9 percent, 17 percent, 32 percent, and 11 percent of the gender gaps in verbal, mechanical, science, and interpersonal tasks, respectively, while they push the math gender gap in the wrong direction. 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, for example, including all five skill measures still explains a portion of the gap in interpersonal tasks, largely because the verbal and mechanical scores have significant effects on interpersonal tasks.
Although my focus in this paper is on occupations, it is useful also to do this analysis for wages. Table A4 shows that while including AFQT explains none of the gender wage gap (consistent with Altonji and Blank 1999), including all ASVAB scores accounts for less than 10 percent of the gap, or less than they can account for the occupation gaps. This implies that occupations explain only a small part of the overall gender wage gap, which is confirmed in Column 4, in which I control for occupation tasks as well as the test scores. Controlling for scores and tasks together explains only 24 percent of the gender wage gap, consistent with other findings in the literature. (For example, Blau and Kahn 2007 find that occupation can account for 27 percent of the gender wage gap.)
Policy discussions about gender gaps in occupation outcomes often focus on particular sets of occupations dominated by one gender, such as STEM (science, technology, engineering, and mathematics) occupations.40 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.41 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, construction workers and scientists and engineers are more likely to be male while teachers are more likely to be female. The AFQT score explains none of the gender gaps for teachers and construction workers, and 23 percent of the gap among scientists and engineers.
Race and Gender Gaps in Selected Occupations
Adding the wider set of ASVAB scores accounts for a much larger portion of all three gaps, including 71 percent 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 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. This exercise shows us that women’s underrepresentation in science and engineering occupations is due not only to their lower science and mechanical skills but also to their higher verbal skills, which push them into other types of occupations.42,43
VI. Results: Career Progression
A. 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 pre-market 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 measures, 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 IV to control for changing demand conditions over time. I focus first on the specific skill measures (the ASVAB scores and noncognitive skill measure). For four of the five skills, there is no evidence that the task gradient is related to the worker’s level of pre-market skill; the coefficients on the own-skill interacted with experience are zero. 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.
Skill-Task Relationships over the Course of a Career
Education, which has a large initial effect on tasks, also has some effect on the task gradients. Somewhat surprisingly, more educated workers see slower growth in most tasks, although the difference is small. Taking the coefficients in Column 6 (on the sum of tasks), a worker with an extra year of education would see his task advantage eliminated in 95 years (holding all other measures constant).44
The race and gender results in Table 6 are similar to the ASVAB score results. The interactions of race and gender with experience have only small effects. However, because many of the skill variables are correlated (for example, 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 6.45 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 (for example, men vs. women) holding all other characteristics fixed. I estimate these paths on a set of eight experience category dummies, instead of a quadratic, to allow more flexibility. The intercept term in the graphs is the average of the fixed effects for that group.46
Estimated Paths of Tasks by Gender
Initial occupation differences between men and women change only slightly with experience. For instance, the average gap in science tasks between men and women is 0.333 standard deviations initially; after 25 years, it is 0.371 standard deviations. The interpersonal gap shrinks from 0.465 standard deviations (in favor of women) to 0.438.47 In all cases, the initial gender gaps in occupation tasks are far larger than any differential changes over the course of a career. Paths in Figure 3 are essentially parallel. Occupation task gaps by race (Figure 4) and education (Figure 5) are also largely stable over the course of a career.
Estimated Paths of Tasks by Race
Estimated Paths of Tasks by Education
Although my focus in this paper is on occupation characteristics, it is useful to compare these measures with wages. Figures 3 through 5 also include the estimated log wage paths for each group. In contrast to the occupation measures, wage paths are not generally parallel; the white-black log wage gap almost doubles in the first ten years, for example, and wages for the high-education group grow much faster than for other groups. The gender log wage gap is fairly stable over a career. From these results, it is clear that factors beyond changes in occupational tasks play a role in driving wage paths.
Overall, initial gaps in occupation persist almost perfectly. Even after 25 years of experience, a worker’s ASVAB scores, race, and gender are strong predictors of his occupation. One implication of these findings is that sorting of workers into occupations on these observable factors happens instantly upon labor market entry, and does not appear to be a gradual learning process. There is no hint here that workers are unsure about their suitability in different occupations.48
Using the model to interpret the career progression results, it appears that learning-by-doing in specific skills is not driving career occupation paths. Recall that in the model, learning-by-doing predicted that initial gaps in tasks would widen. Here, I have found that these gaps do not widen or shrink. Instead, the career progression pattern is what would be predicted by an increase in general skill—and no differential increase in specific skills—as experience grows. It may be that general skill is growing for all workers as they gain experience, leading them to increase their math, verbal, science, and interpersonal tasks (tasks positively associated with education in Table 3) and decrease their mechanical tasks, which are negatively associated with education. In the next section, I discuss some other explanations for parallel occupation paths across workers.
B. Alternative Explanations for Similar Career Paths by Education Level
It is somewhat surprising that high-skilled workers do not see faster occupational progression, particularly given their faster growth in wages. 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 workers 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 employers (such as education) become less important over time as employers learn about harder-to-observe elements of ability, such as the ASVAB test scores (Altonji and Pierret 2001; Light and McGee 2015). However, I do not find that the ASVAB scores have an increasing effect on occupation content, so something else must be driving my results.49
A second possible explanation 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 three-digit occupation codes. Unfortunately, the data do not provide a finer level of occupational detail, and thus I cannot evaluate this possibility in this paper.
A third possibility is that some high-education workers are in the highest-task occupations, 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 increases because no higher-math occupation exists.50 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 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.
Table A7 has the results. The 99th percentile of math tasks for the high-education group starts at a very high level of math tasks, so it would be difficult for these workers to move to higher-math occupations.51 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. At the lower end, where this constraint would not be relevant, more educated workers do see faster task growth. Thus, hitting a “task ceiling” seems to be part of the story of the lack of educational differences in task gradients. Even at the median, however, the more educated workers see slower progression, so this cannot be the whole story.
C. Average Career Paths
The results of Section VI. A suggest that there are only 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 (such as education and test scores) and unobservables, I estimate the career paths of each task for the pooled sample using worker fixed effects. I again control for the task demand measures described in Section IV.52 The regression equations (one for each task measure) are
(18)Table 7 has these results. Math, verbal, science, and interpersonal tasks grow substantially with experience for the average worker while mechanical tasks decline with experience. Generally speaking, workers move to occupations that require more of most types of tasks as they gain experience.53
Experience Profiles of Each Task, with Worker Fixed Effects
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 0.771 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 0.349 higher total tasks. This implies that 25 years of career progression in occupations is equivalent to the effect of about 2.2 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 most as they gain experience. Figure 6 shows the fraction of workers in management or supervisory occupations at each value of experience, separately by education level. Consistent with the occupational choice results, workers with more education are more likely to be in management occupations.54 All education groups move into management and supervisory positions more as they gain experience. What is striking is that, consistent with the results of Table 6, the rates at which each group moves into management are similar (the lines are essentially parallel).
Fraction Working as Managers or Supervisors
An 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 1996), 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. This is possible but seems unlikely.
D. Application: The Effect of Layoffs on Career Paths
Having established the task content of a typical career trajectory, it is interesting to use this framework to study the effects of layoffs on career paths. The model gives no hint at what effect of a layoff one might expect, so this is purely an empirical exercise. It is well known that workers who are laid off suffer large and persistent earnings losses (Jacobson, LaLonde, and Sullivan 1993) 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.55
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 reestimating 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, and if the effect on wages is more or less persistent than the 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.56 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 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 two years ago,” “laid off three years ago,” and “laid off four years ago.” These regressions also include worker fixed effects so the estimates can be interpreted as the causal effect of a layoff within a typical worker’s career path.
Effects of Layoffs on Experience Paths
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 that uses lower levels of math, verbal, science, and interpersonal tasks. The initial effect on the sum of tasks (Column 6) is a loss of 0.184 standard deviations in total tasks, which is about one-fourth of the total 25-year increase in task content estimated in Table 7.57
However, the effect of a layoff on occupation content is short-lived. About 30 percent of the effect of a layoff on occupation tasks is gone after the second year, and there is no significant effect after three years. I do not find any evidence here that laid-off workers are pushed permanently off their occupational career path.58
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 (and again includes worker fixed effects). The effect of a layoff wages decays as the worker recovers from the layoff but it is still significant four years after the layoff or after the effect on occupation has worn off.
Effects of Layoffs on Wages
In Columns 2 and 3 of Table 9, the dependent variable is the predicted wage from regressions of wages on the skill measures, education, and occupation task measures (the dependent variable in 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 that the effect of a layoff on occupation tasks accounts for only a modest portion—around 20 percent—of the total effect of a layoff on wages. One explanation for this 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).59
VII. Conclusion
This paper develops a new 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 a portion of the race and gender gaps in occupation content, including 71 percent of the gender gap in science and engineering occupations.
Furthermore, it is not simply the level of pre-market skills which matters but the types of skills. Whether a worker is of higher ability in science or reading and writing has implications for his choice of occupation throughout his career. Skills are multidimensional, and the dimensions matter. This is particularly relevant in understanding the differing occupational outcomes of men and women.
As careers progress, workers increasingly move to occupations that require more math, verbal, science, and interpersonal tasks, and fewer mechanical tasks. Career patterns are remarkably similar across all types of workers so that initial differences in occupations, including those by race and gender, 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 three years, the effect of the layoff on occupation content is mostly gone, and this accounts for only about 20 percent of the layoff’s effect on wages.
I have used this paper’s framework to study two policy-relevant issues: race and gender gaps in occupation content and career progression, and the effects of layoffs. The framework is useful for studying a variety of other questions and applications, which I leave for future research.
Acknowledgments
He thanks Joseph Altonji, Lisa Kahn, and Fabian Lange for their guidance and support on this project, as well as Erica Blom, Mark Klee, Seth Zimmerman, Chris Neilson, Martin Hackmann, Rebecca Edwards, Treb Allen, Adam Osman, Giuseppe Moscarini, Chris Robinson, Nick Kanamaru, and two anonymous referees for their valuable suggestions. Finally, he is grateful to David Autor for his help with the O*Net data in the early stages of this project. All errors are the author’s own. The data used in this article can be obtained beginning December 2017 through November 2020 from Jamin D. Speer, Fogelman College of Business and Economics, University of Memphis, Memphis, TN 38152, or by emailing jspeer{at}memphis.edu.
Appendix 1
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 output xiγ produced by worker i in occupation γ is
(18)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—sij for j and sik for k. Second, general skill sig makes a worker more productive in performing both tasks.
A. Demand for Tasks
Demand for output comes from outside the model. The price of occupation γ’s output xγ is
(19)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.
B. 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
(20)This is the price of the output times the amount produced by the worker. The log wage of worker i in occupation γ is
(21)The wage function is an equilibrium condition that reflects the demand for output and the production function relating tasks j and k and the worker’s skills to output.
C. 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
(22)
(23)The task choices are a function of the workers’ skills and the β terms, which represent demand for each task.
Let ln Pxy*=P( jγ*(sij, sik, sig; β1), kγ*(sij, sik, sig; β2)). In equilibrium, then, wages for worker i in his optimal occupation are
(24)Therefore, wages in equilibrium are a function of the worker’s skills and demand conditions for each type of task j and k.
D. An Example
Suppose that the log of the production function f is
(25)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 (that is, 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 from the average.
Also suppose that the price of an occupation’s output can be written as
(26)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 that uses task levels jγ and kγ is
(27)This is the wage function given in the model of Section II. 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, 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.
Appendix 2
O*Net Task Measures and Descriptions
A. 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.
B. 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.
C. 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).
Operating Vehicles, Mechanized Devices, or Equipment: Running, maneuvering, navigating, or driving vehicles or mechanized equipment, such as forklifts, passenger vehicles, aircraft, or watercraft.
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
D. 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.
E. Interpersonal Tasks
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.
Skill and Task Correlations
Correlations Between Tasks and an Occupation Earnings Measure
Early-Career Occupational Choice Regressions, with Knots at 0 Scores
Race and Gender Gaps in Wages
Summary Statistics for Expanded Sample
Selected Gaps in Task Content, by Experience Level
Experience Profiles of Math Tasks, by Percentile
Experience Profiles of Each Task, with Worker Fixed Effects (and No Task Demand Measures)
Footnotes
↵1. Light and McGee (2015) also combine the full set of ASVAB scores with O*Net data to study the determinants of the rate of employer learning. Their focus is on wages, rather than occupational outcomes. Boehm (2015) uses the full set of ASVAB scores to study sorting into high-, medium-, and low-skill occupations but does not consider the match between skills and tasks.
↵2. Blau et al. (1956) propose a broader occupational choice framework, which accounts for skills, personality traits, discrimination, and other factors. I consider only skills here although I discuss how these other factors may be affecting my results.
↵3. An exception to this is Boehm (2015), who uses the NLSY’s ASVAB scores and noncognitive skill measures to analyze sorting into high-, middle-, and low-skill occupations.
↵4. In the empirical analysis, an occupation will require more than two types of tasks, and a worker will have more than two types of specific skills. I use a two-task model here for ease of exposition.
↵5. See Acemoglu and Autor (2011) for a more complete treatment of the supply and demand for tasks.
↵6. The expanded model in Appendix 1 discusses how changing demand conditions would affect the wage coefficients.
↵7. The basic structure and intuition of the wage function are adapted from Altonji (2005), who analyzes the choice of occupations along a single dimension.
↵8. The wage in occupation γ is not generally equal to zero if the worker has zero skill. It is useful to interpret the skills as deviations from the mean skill so that the wage in occupation γ at sj = sk = sg = 0 is the wage for the average worker if he chooses that occupation.
↵9. The 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. The implications of such a setup the same.
↵10. An alternative formulation would include a time budget constraint for tasks. As I discuss in the data section, my occupation task data do not distinguish between changes in task amount and task level, making it difficult to interpret a budget constraint for tasks. The model I use here is similar to a formulation which omits the α7 and α8 terms and instead includes a budget constraint in which the worker’s general skill level serves as the constraint for how many tasks a worker may take on. Predictions from such a model are nearly identical to the model I consider here.
↵11. Throughout the analysis, I will assume that │α9│ is small enough that the denominator is positive.
↵12. One also could 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.
↵13. These implications are made stronger if the two tasks are substitutes and weaker if they are complements. Even for strong complements, however, initial differences grow if μ1 > 0 and π1 > 0.
↵14. Because skill growth is linearly related to occupation in this simple model, having μ1 < 0 and π1 < 0 would imply that occupation paths for workers who start in different occupations cross at some experience level. While this is possible, I am focused here on the period of experience over which the gaps would be shrinking.
↵15. The NLSY97 respondents have been interviewed annually since 1997. The NLSY79 respondents were interviewed annually from 1979 to 1994 and biennially since 1994.
↵16. This restriction has little effect on the results.
↵17. Restricting the NLSY79 to workers who entered the labor market after taking the ASVAB produces a sample weighted toward more educated workers.
↵18. A complete list of military occupation requirements is available at http://www.military.com/join-armed-forces/asvab.
↵19. Results are similar when electronics information is included in the mechanical composite rather than the science composite.
↵20. Boehm (2015) uses similar ASVAB score combinations (math, verbal, and mechanical) to analyze sorting of workers into high-, middle-, and low-skill occupations.
↵21. Unfortunately, no comparable measures are available in the NLSY97. For all NLSY97 respondents, I set interpersonal skill equal to the mean value from the NLSY79.
↵22. See Heckman, Stixrud, and Urzua (2006) for more details on the Rotter and Rosenberg measures.
↵23. Education likely contains information about both general skill and specific skills, depending on what these workers chose to study in school. In empirical results I do not show here, I find that the ASVAB scores are strong determinants of college major content. This suggests that the information that would be conveyed about specific skills by education is largely captured by the ASVAB scores themselves.
↵24. This definition of labor market transition is similar to those used Farber and Gibbons (1996) and Schönberg (2007). Results are similar with different definitions. About 5 percent of workers return to school after making this transition. I keep counting their experience even when they have returned to school.
↵25. By “whites,” I actually mean those who are nonblack and non-Hispanic. By “blacks,” I mean non-Hispanic blacks. These distributions are plotted for the sample I use for my analysis, rather than for the whole NLSY. Therefore, the means for each group may not average out to 0, the overall mean.
↵26. To my knowledge, no previous paper has attempted to explain occupational differences between men and women using the AFQT or the ASVAB.
↵27. As noted by many researchers, surveys like the NLSY are riddled with measurement error in the coding of occupations. Measuring occupations by task requirements may lessen this problem, however. If an occupational change is recorded when none actually took place, it is likely that the new coded occupation is similar in task content to the previous coded occupation.
↵28. Occupation-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 within occupation.
↵29. Each task gives an “importance” and “level” measure; I use both measures. Results are generally not sensitive to this choice, as the importance and level measures are highly correlated.
↵30. In 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 and fine motor skills. This is the approach taken in Poletaev and Robinson (2008) and Robinson (2010). The other approach is to choose task categories ex-ante and then 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 the two techniques but is closer to the latter.
↵31. O*Net measures are at the level of SOC codes while the NSLY occupations are at the three-digit Census code level. I crosswalk the two using the mapping provided by Ruggles et al. (2015).
↵32. The 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 to 59 working fulltime and to years 1980 to 1999.
↵33. I also regress the sum of all five tasks on the skill measures and education to give a sense of the effect of skills on the total level of tasks. I do this to provide a benchmark measure of the total effect of education on tasks, which I will use later to compare with the effect of experience on tasks.
↵34. I use this definition of early career instead of just the initial occupation to achieve a larger sample size. Results are almost identical when I use experience 0 to 1, or experience 0 to 3.
↵35. This method of describing career progression – estimating how task measures change with experience – is similar in spirit to the methodology used by Yamaguchi (2010b). My task measures are more detailed, however, and are linked to the worker skill characteristics. This allows me to test career path differences across workers in the manner predicted by the model.
↵36. Boehm (2015) also analyzes occupational sorting patterns using ASVAB scores and finds results consistent with those of this paper. He finds that that math scores predict going into high-skill occupations, verbal scores predict going into high- and low-skill occupations, and mechanical scores predict going into medium-skill occupations. My results add to these findings by also considering the task content, rather than simply the “level,” of the occupation.
↵37. All results in Table 3 are robust to including a full set of education dummies instead of a single variable for education. When these regressions are performed separately for different levels of education, I find positive (significant) sorting of skills to tasks for all groups, with a few interesting differences. Math-to-math sorting is strongest for the high-education group while mechanical sorting is strongest for the low-education group. These results are available upon request.
↵38. See 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 and service occupations, for example – and that blacks and Hispanics are found in lower-skill occupations. Women also may be found in occupations with lower promotion possibilities (Paulin and Mellor 1996) and lower value to the firm (Schumann, Ahlburg, and Mahoney 1994).
↵39. Large 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) in mechanical and science scores, respectively, are 0.75 and 0.48 in the NLSY79 and 0.32 and 0.21 in the NLSY97.
↵40. See, for example, The White House (2012).
↵41. In my sample, males constitute 18 percent of teachers, 97 percent of construction workers, and 80 percent of scientists and engineers.
↵42. I include education in all of these regressions because while education partially reflects choices made by the worker, the same is true for the ASVAB scores. If education is not included, results are similar; the ASVAB scores account for 77 percent of the science and engineering gap.
↵43. Although these regressions are pooled across the NLSY79 and NLSY97, there is heterogeneity in effects across the two surveys. Both the gender gap in science and engineering and the degree to which ASVAB scores can account for this gap are smaller in the NLSY97. In the later survey, ASVAB scores account for about half of the gender gap in science and engineering. However, a full comparison between the two NLSYs is not possible yet because the younger NLSY97 respondents still may be in graduate programs that lead to science and engineering occupations.
↵44. It is important to emphasize that these are partial effects. Highly educated workers also have high verbal test scores, for example, and the interaction of verbal scores and experience has a positive effect on task growth that would oppose the negative effect of the education-experience interaction.
↵45. Here, education is divided into three categories: high (16 years and above), medium (13 to 15 years), and low (12 or fewer years).
↵46. These regressions also include the task demand measures. I also include workers who took the ASVAB after entering the labor market, who were excluded in the prior results. I include them here because they help produce a more balanced sample to estimate effects at higher levels of experience. Without them, the sample is weighted more heavily toward workers with higher education, which makes it difficult to estimate task effects at high levels of experience. When these workers are excluded from these regressions, estimates at low levels of experience are similar, but the estimates at high levels of experience are very imprecise. Also, I am not concerned here about the effects of work experience on test scores, which was the reason for excluding these workers from prior analysis. Table A5 has summary statistics for this expanded sample.
↵47. Table A6 reports, for race, gender, and education level, the estimated average gaps at 0, 5, 10, 20, and 25 years of experience for each task.
↵48. Sorting may be more gradual on less observable skills and occupation characteristics that I do not consider here.
↵49. When I repeat the analysis of Table 6 with wages as the dependent variable, I find results in line with Altonji and Pierret (2001); education reduces the wage gradient while test scores (particularly math and verbal scores) increase the wage gradient. The fact that results differ for wages and occupation characteristics suggests that some learning takes place within (and not across) occupations, and is an interesting topic for future research.
↵50. A mathematician may upgrade his math task content within occupation by taking on more math tasks (or more difficult math tasks) but this would not show up in the occupation codes.
↵51. This is particularly true because of possible educational requirements for entering top-level occupations. These requirements are not included in the model but in reality, it would be difficult for a worker to move into an occupation which usually requires an advanced degree.
↵52. For these regressions, as in Figures 3 through 5, I also include workers who took the ASVAB after entering the labor market to achieve a more balanced sample.
↵53. Table A8 repeats this regression without the task demand measures. Results are qualitatively similar but the estimated task changes without the demand measures are about 50 percent larger. It is evident that some of the realized career task changes of these workers was driven by changing demand for tasks as their careers progressed.
↵54. The relationship is not monotonic if the education groups are more disaggregated. Those with exactly 16 years of education are more likely to be managers than those with more than 16 years.
↵55. Poletaev and Robinson (2008) show that displaced workers generally move to occupations that require less skill. 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. See also Gathmann and Schönberg (2010) for analysis using German data.
↵56. I categorize both plant closings and firings as layoffs. Temporary jobs that have ended are not counted as layoffs.
↵57. The estimates of career changes in tasks are slightly smaller in Table 8 because they do not include the first few years of the NLSY79, which are associated with fast task growth. This regression thus underestimates total career task growth.
↵58. In results I do not show here, I find that the effects of layoffs on occupation content are generally unrelated to the worker’s premarket levels of skill.
↵59. Poletaev and Robinson (2008) and Neal (1995), among others, show that the degree of occupational displacement associated with a layoff – say, the change in tasks from the pre-layoff to post-layoff occupation – is related to the wage change. My analysis does not contradict these results; it merely shows that the occupation effect accounts for only a modest portion of the total wage effect. Also, my regressions in Tables 8 and 9 include worker fixed effects and so do not measure heterogeneity across workers.
- Received February 2015.
- Accepted July 2015.
