Pre-Market Skills, Occupational Choice, and Career Progression

Transcription

1 Pre-Market Skills, Occupational Choice, and Career Progression Jamin D. Speer Yale University January 2014 Abstract This paper develops a new theoretical and empirical framework for analyzing occupational choice and career progression, focusing on the role of pre-labor market skills in determining career outcomes. I propose a model of occupational choice in which a worker s skill vector determines his choice of occupation tasks. Skills grow with experience through learning-by-doing in a way that may be related to the initial occupation. To obtain a rich account of pre-market skills and individual career trajectories, I merge the NLSY79 and 97 with O*Net data on the task content of occupations. I find that pre-market skills as measured by the ASVAB test scores (math, verbal, mechanical, and science) and an interpersonal skill measure predict the corresponding task content of the workers initial occupations, even after controlling for general skill measures like education. I then ask how the relationships between skills and occupations evolve as workers gain experience. Pre-market skills have long-lasting effects on career outcomes. Career trajectories are similar across worker skill types, implying that initial differences in occupation persist over the course of a career. The change in the tasks performed by a typical worker over the first 25 years of his career is equivalent to the difference in tasks associated with about 2.3 years of education. I provide two policy-relevant applications of jamin.speer@yale.edu, Webpage: 1

2 this framework. First, I study the role played by pre-market skills in the differing occupational outcomes of men and women. The ASVAB scores account for a portion of occupational gender gaps, including 70% of the gap in science and engineering occupations. Occupational gender gaps also persist over the course of a career. Second, I quantify the effect of layoffs on occupational attainment and career trajectory. I find that a layoff erases about one-fourth of a worker s total career increase in task content, but within 3 years, this effect is typically undone. 1 Introduction The question of why workers do the jobs they do is fundamental to understanding how labor markets function. In this paper, I ask two questions. First, to what extent can prelabor market skills account for variation in occupation choice? Second, how persistent are initial differences in occupation over the course of a career? This paper develops a new theoretical and empirical framework for analyzing occupational choice and career progression, focusing on the role of pre-labor market skills in determining career outcomes. I develop a model which illuminates the relationships between a worker s skill set and his choice of occupation. Using a novel combination of data on workers skill portfolios with data on the task requirements of their occupations, I find a strong role for skills in the initial occupation choices of workers. I also show that career trajectories are similar across workers, meaning that pre-market skills are 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 NLSY79 and NLSY97) with data on the task requirements of their occupations (O*Net). The NLSYs provide me with a set of pre-market skill measures (the ASVAB test scores) for a panel of individuals whose careers I can see unfold over several decades. The O*Net data allow 2

3 me to determine what types of tasks individuals are performing at different stages of their careers. Together, these data sources allow me to examine in detail how pre-market skills and occupation choices interact in forming individuals careers. In particular, I can ask how a worker s test score in a given field (e.g., math) is related to the task content of that field in his occupation, and how this relationship changes over the course of his career. I develop a model of occupational choice and career progression in which a worker is characterized by a vector of skills and an occupation by a vector of tasks. Skills are the abilities of the worker, either endowed or learned, while tasks are the activities required in an occupation to produce output. The worker s optimal choice of occupation depends on how his skill vector matches with the tasks required in the occupation, as well as the market returns to those tasks. A worker s skills grow through learning-by-doing in a way that may be related to his initial occupation choice. The model has implications for both initial occupation choice and career trajectory. Pre-market skills, including skills specific to one field and more general skills, should predict initial occupation choice. As careers progress, initial differences in occupation choice may widen, shrink, or persist perfectly over the course of a career depending on how skill accumulation is related to the initial choice of occupation. First, I find that pre-market skills as measured by the ASVAB components (math, verbal, mechanical, and scientific aptitude), and an interpersonal skill measure, predict the task content of the workers initial occupations, even after holding constant measures of general skill such as education. Workers higher in verbal skill, for example, enter occupations which use more verbal tasks, holding all else equal. It is not simply a worker s level of skill that determines occupation choice, but the types of skills he has. I apply this framework to study the differing occupation outcomes of men and women. I show that men are found in more mechanical- and science-intensive occupations, while women are found in occupations requiring more math, verbal, and interpersonal tasks. I ask if these gaps can be explained by differences in pre-market skills between men and women. In the ASVAB, women score higher on the verbal tests, while men score higher on the mechanical and science tests, particularly at the top of these distributions. 3

4 Differences in ASVAB scores account for a portion of occupational gender gaps, including 70% of the gender gap in science and engineering occupations. Including only the AFQT score (a commonly used composite of the math and verbal ASVAB components) accounts for only little of these gaps. Second, having established the links between skills and initial occupation choice, I ask how these relationships evolve as workers gain experience. I develop a method for describing career paths empirically by quantifying how the task content of a worker s occupation changes with experience. I show that career trajectories are similar across worker skill types and across race and gender, implying that initial differences in occupation persist over the course of a career. As careers progress, workers of all types increasingly move to occupations which require more math, verbal, and interpersonal tasks, and fewer mechanical tasks. The change in the tasks performed by a typical worker over the first 25 years of his career is equivalent to the difference in tasks associated with about 2.3 years of education. I apply the career progression framework to study the effect of layoffs on a worker s career path. It is well known that layoffs can have persistent negative effects on earnings (e.g., Jacobson, LaLonde and Sullivan (1993), von Wachter (2012)), but less is known about the mechanisms behind this effect, including potential impacts on occupations and career paths. I find that a layoff erases about one-fourth of a worker s total career increase in task content. However, that effect is short-lived. After 3 years, the effect of the layoff on occupation content is mostly undone. On the other hand, the negative effects of a layoff on wages outlast the effects on occupation tasks, suggesting that occupation content is not the only mechanism driving these wage effects. The initial effect of a layoff on occupation content can account for about 20% of the initial effect on wages. These two applications of my framework gender gaps in occupation outcomes and the effects of layoffs are quite different, which is a testament to the applicability of the framework to a variety of policy-relevant questions. While the NLSY (especially the NLSY79) has been used extensively by researchers, my use of the ASVAB scores to analyze occupational sorting and career paths is novel. The results show that pre-market skills in a variety of different fields play an important 4

5 role in the career outcomes of workers, including the differing occupational outcomes of men and women. Utilizing the wider set of ASVAB scores, rather than just the AFQT score, significantly improves our understanding of these outcomes. The study of occupational choice has a rich history in economics, and economists have long recognized skills an important determinant of these choices. Roy (1951) develops a model in which workers have 2 skills, and comparative advantage and the returns to skills determine which sector the worker enters. Heckman and Sedlacek (1985) present a model which allows for multiple skills, both observed and unobserved, which have varying usefulness in different jobs. 1 occupation characteristics is rare. Still, empirical evidence linking worker skill portfolios to This paper builds on both Roy (1951) and Heckman and Sedlacek (1985). I consider a broad set of worker skills and characterize occupations on a multi-dimensional continuum of task content. I then combine data sources in a novel way to provide empirical evidence on the relationships of workers skill vectors to occupation choice. The economics literature has also documented that workers change occupations often (e.g., Miller (1984), Kambourov and Manovskii (2008)). Economists have interpreted the pattern of frequent job changes in many ways: as a search process for a better match (Jovanovic (1979), Neal (1999)), as workers learning about their own skills (Gibbons, Katz, Lemieux and Parent (2005), Papageorgiou (2012), James (2012)), as employers learning which workers are worthy of promotions (Jovanovic and Nyarko (1997)), or as evidence of skill accumulation (Rosen (1972), Sanders (2012)). I contribute to the occupational choice and mobility literatures by developing a framework linking pre-market skills to occupation choices over the course of a career, and by combining data sources to quantify the effects of these skills. Instead of focusing on the determinants of individual occupational changes, I focus on the broad patterns that characterize career paths, and I ask whether skill measures predict deviations from these broad patterns. Other types of models, particularly those that emphasize worker or employer learning, are complementary with my framework. I provide a description of 1 Blau et al. (1955) propose a broader occupational choice framework, which accounts for skills, personality traits, discrimination, and other factors. I consider only skills here, although I discuss how these other factors may be affecting my results. 5

6 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 (e.g., Yamaguchi (2010b), Yamaguchi (2012)). By characterizing an occupation as a bundle of tasks, one can study the relationship of different occupations and more meaningfully look at mobility patterns. However, this literature has not to this point focused on understanding what types of workers enter each type of occupation. In some cases, occupation tasks are used as a proxy for the worker s skills (Ingram and Neumann (2006), Robinson (2010)), but evidence on sorting patterns is required to justify this assumption. By combining occupation task data with data on a variety of pre-market skill measures, I provide some of this evidence. While the occupation task literature provides an interpretation for individual occupational changes, a framework for interpreting a worker s entire career remains elusive. A recent paper by Sanders (2012) merges the NLSY with O*Net data and interprets changes in tasks over a career as a combination of skill accumulation and learning. He does not consider the matching of skills to tasks. I add to this work by considering the determinants of initial occupation choice and career trajectory jointly, and by providing empirical evidence on how skills affect these patterns. This paper also contributes to the literature on the effects of pre-market skills for later outcomes. A series of papers by Heckman, including Heckman, Stixrud and Urzua (2006), has shown that both cognitive and non-cognitive abilities have impacts on workers later outcomes. Neal and Johnson (1996), using the NLSY, show that AFQT scores can account for much of the wage gap between blacks and whites. I add to this literature by measuring the effects of a wide array of pre-market skill measures on occupation choices and showing how those effects persist over the course of a career. 6

7 The paper proceeds as follows. Section 2 presents a model of occupational choice and the determinants of career progression. Section 3 describes the data sources, and section 4 describes the empirical strategy. Sections 5 and 6 present the results, which include applications of the occupation choice and career path framework. Section 7 concludes. 2 A model of occupational choice and career progression 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. 2.1 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 either specific or general. A specific skill is only useful in performing a given task; an example might be knowledge of how to operate a hand saw. A general skill is useful in performing any task. An example of a general skill might be problem solving ability, which makes a worker more productive in whatever task he is performing. 7

8 An occupation requires two types of tasks j and k. A worker has skills (s j,s k,s g ). The terms s j and s k denote specific skills, useful in performing tasks j and k, respectively, while s g denotes general skill, useful for performing both j and k. 2 General skill may be correlated with specific skills, but is not a function of specific skills, and vice versa. A worker chooses an occupation a vector (j,k) to maximize his wage. Wages are determined by supply and demand for tasks. In Appendix A, I provide a simple model of wage determination, based on Altonji and Rosenzweig (2007). 3 Workers use skills to perform tasks, which are the intermediate inputs used to produce output. Firms sell output to the market, and demand for this output drives demand for tasks. Labor markets are perfectly competitive spot markets, so that workers are paid their marginal product in each period. The wage function is an equilibrium condition that reflects (1) the demand for the final output that tasks are used to produce, (2) the production function relating a worker s skills and the tasks he performs to his output, and (3) the supply of workers with each type of skill. Worker i s output x in occupation γ, which requires tasks j γ and k γ (e.g., math and interpersonal activities), is x iγ = f(s ij, s ik, s ig ; j γ, k γ ). The production function f has two key features. First, higher levels of each specific skill makes a worker more effective in performing the associated task s j for task j and s k for task k. Second, higher general skill s g makes a worker more effective in performing both tasks j and k. The production function has the same form for all occupations, and only differs by the levels of j and k each occupation uses. On the demand side, let us assume that the price of the output of an occupation can be approximated by a flexible function of tasks j and k. Occupations differ only by the levels of j and k that they require. For a suitable formulation of the production function and of demand for output (see Appendix A), the following flexible log wage formulation 2 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. 3 See Acemoglu and Autor (2011) for a more complete treatment of the supply and demand for tasks. 8

9 results for worker i in an occupation γ which uses task levels j γ and k γ : ln(w iγ ) = α 1 j γ α 2 j 2 γ + α 3 s ij j γ + α 4 k γ α 5 k 2 γ + α 6 s ik k γ + α 7 s ig j γ + α 8 s ig k γ + α 9 j γ k γ. 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. 4 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 s j and task j, which comes from the worker s production function. The next three terms are analogous to the first three for k. If skill-task complementarity is more important for one task than another, α 3 and α 6 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, α 7 and α 8 may differ. 5 coefficients are assumed to be positive. The first eight A skill is not valuable unless it is applied to a task. If a worker with some skill s k were to choose an occupation which uses none of task k, then he would not be paid for his skill s k. Note also that the wage is zero when the worker chooses an occupation which requires zero levels of j and k. 6 The final term reflects how j and k are priced in equilibrium, which is determined by the distribution of demand across occupations. If demand for output tends to be higher in occupations which use higher levels of both tasks, then α 9 > 0. If, on the other hand, demand is higher for output of occupations that use one task or the other, but not high 4 The expanded model in Appendix A discusses how changing demand conditions would affect the wage coefficients. 5 The basic structure and intuition of the wage function are adapted from Altonji (2005), who analyzes the choice of occupations along a single dimension. 6 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 s j = s k = s g = 0 is the wage for the average worker if he chooses that occupation. 9

10 levels of both, then α 9 < 0. When α 9 > 0, I refer to the tasks as complements, and when α 9 < 0, I refer to the tasks as substitutes. 7 A low-skill worker will find himself unproductive in a high-task occupation. In terms of task j, the second term ( α 2 j 2 ) ensures that not all workers will opt for the highest j possible, while the third term (+α 3 s j j) and seventh term (+α 7 s g j) ensure that moreskilled workers will choose higher-j occupations (ignoring effects of task substitutability). Similar statements can be made for task k 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 α 1 2α 2 j + α 3 s j + α 7 s g + α 9 k = 0 α 4 2α 5 k + α 6 s k + α 8 s g + α 9 j = 0 which, after solving and substituting, lead to solutions of j = 2α 1α 5 + α 4 α 9 + 2α 3 α 5 s j + α 6 α 9 s k + s g (2α 5 α 7 + α 8 α 9 ) 4α 2 α 5 α 2 9 (1) k = 2α 4α 2 + α 1 α 9 + 2α 6 α 2 s k + α 3 α 9 s j + s g (2α 2 α 8 + α 7 α 9 ). (2) 4α 2 α 5 α9 2 The solutions provide information about the relationships between each skill and its 7 The term α 9, 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. 8 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 α 7 and α 8 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. 10

11 own task, each skill and the other task, and general skill and each task. 9 I discuss each of these relationships separately Sorting: skills to tasks First, the relationship between each specific skill and its associated task is positive. j s j = 2α 3α 5 4α 2 α 5 α 2 9 k s k = 2α 6α 2 4α 2 α 5 α 2 9 The effect of s j on j is unambiguously positive, and is increasing in α 3 (the degree of complementarity between s j and j in production) and in α 5, which reflects the degree of diminishing returns to task k. Second, the relationship of a specific skill with the other task depends on whether the > 0 > 0. two tasks are substitutes or complements. Specifically, j s k = k s j = α 6 α 9 4α 2 α 5 α 2 9 α 3 α 9 4α 2 α 5 α Because of the relationship of j and k in demand for output, a specific skill affects the choice of both tasks, despite only being useful in its own task. The signs of these relationships depend on the sign of α 9. If two tasks are substitutes (α 9 < 0), then each skill affects the other task negatively. This is the logic of comparative advantage. If two tasks are complements (α 9 > 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. 9 Throughout the analysis, I will assume that α 9 is small enough that the denominator is positive. 11

12 Third, the relationship between general skill s g and each task is ambiguous. The derivatives are j s g = 2α 5α 7 + α 8 α 9 4α 2 α 5 α 2 9 k s g = 2α 2α 8 + α 7 α 9 4α 2 α 5 α If the two tasks are complements, then the relationships are clearly positive; higher general skill will raise the optimal choice of both tasks. Workers of higher general skill would be found in higher-j, higher-k occupations. If, however, they are substitutes, the relationship is unclear. General skill will negatively predict j and k, respectively, if and α 9 < 2α 5α 7 α 8 α 9 < 2α 2α 8 α 7. 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 (α 7 is large and α 8 is small). Then it may be the case that general skill raises the optimal choice of j but decreases the optimal choice of k. Workers of high general skill would be found in high-j, low-k occupations. I have assumed that occupations have full support over (j,k). In the case that general skill is positively related to one task and negatively related to the other, there will be very few workers found in occupations with high levels of both tasks or with low levels of both tasks. Therefore, the observed support of occupations in (j,k) space will show 12

13 a negative correlation between j and k, and the high-j, high-k (and low-j, low-k) areas will be sparsely populated. Occupations may not have full support over (j,k) because of this. In other words, the actual distribution of j and k in available occupations is an outcome of the model, but my assumption is that any (j,k) pair would be available if the worker wanted to choose it What does the skill vector measure? The vector (s j,s k,s g ) refers to the worker s skills at labor market entry. This includes innate ability, parental investments, and educational investments, including possibly college attendance. Because these skills depend in part on educational choices made by the worker, which may have been undertaken with specific occupations in mind, they are potentially endogenous and should not be taken as randomly assigned to workers. In Appendix C, I provide a model of how a worker makes decisions about college investments based on his pre-college skill set. In this model of college choice, a worker observes his skill vector at the end of high school and makes a decision about whether to attend college, what type of college to attend, and what to major in. The model shows that higher-skill workers are more likely to attend college, and that choice of major is positively related to skills a worker already has (i.e., a worker high in s j is more likely to major in a field related to task j). 10 this is true, then the skills at the time of labor market entry which may include college investments are functions of the pre-college skills. Education increases a worker s skills in a way related to the skills he already had. Therefore, while the skill vector (s j,s k,s g ) is partially the product of a worker s choices, they are choices made based on his earlier skill set. I address this issue further in Section 5.2, where I discuss how to interpret my results. 10 In an ongoing project, I show empirical results that confirm these predictions. College major content is closely related to a worker s test scores measured before college. If 13

14 2.2 Skill accumulation and career progression I now turn to the dynamics of occupation choice over the course of a career. Workers work for T periods and may choose a new occupation in each period at no cost. I denote experience by t < T and assume that workers skills grow as follows: s g,t+1 = s g,t + ψ t s j,t+1 = s j,t + µ 0 + µ 1 j t s k,t+1 = s k,t + π 0 + π 1 k t. Specific skills grow via learning-by-doing as well as an exogenous growth component. General skills grow according to an experience profile ψ t, which I assume is common across all workers. 11 Workers have the incentive to invest in their future skills by choosing higher values of j and k than they otherwise would. The worker s problem is now more complex, as he maximizes the present discounted value of his wages instead of his one-period wage. Because the choice of j in period t affects s j,t+1 and therefore j t+1 and k t+1, the problem is also much more difficult to solve, and the solution is not as elegant as the static solution. Recalling the one-period solution, we can now write the dynamic solution for j in the form j t = 2α 1α 5 + α 4 α 9 + 2α 3 α 5 s jt + α 6 α 9 s kt + s gt (2α 5 α 7 + α 8 α 9 ) 4α 2 α 5 α I t = j static + I t where I t is the investment term, or the difference between his one-period wage-maximizing j and his optimal j in the dynamic problem. 12 The worker now earns a lower wage in 11 One could also imagine that general skill growth is influenced by the occupation choice of the worker. I assume that it is not in order to simplify the analysis. 12 I t > 0 for t < T. In period T, I T = 0 and the worker simply maximizes his final-period wage. 14

15 the early periods, sacrificing some pay for future skill accumulation. The logic here is the same as in a Ben-Porath-type model (Ben-Porath (1967)), in which a worker chooses each period how much to produce and how much to invest in skills. Here, there is no time allocation decision for the worker, but his choice of occupation tasks determines both his wage and his future skill growth. I am primarily interested in the implications of these skill growth patterns for career task progression and for the persistence of initial differences in occupation choice. First, consider the case in which specific skills do not grow (µ 0 = µ 1 = π 0 = π 1 = 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 s g 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 (µ 1 > 0 and π 1 > 0), then workers who begin their careers in higher-j occupations which would include workers with higher initial levels of s j and s g (if s g has a positive relationship with j) will see their skill s j grow faster than those of other workers, which will translate into faster growth of task j in their occupations. Initial differences in occupation choice should widen as experience increases. 13 It could also be the case that skill growth is negatively related to initial occupation (µ 1 < 0 and π 1 < 0) if there are diminishing returns to skill accumulation. In this case, initial occupation gaps will shrink over the course of a career Summary of empirical implications There are two sets of empirical implications from the model. First, I look at the effects of skills on the initial occupation s tasks. The one-period solution for j from equation 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 µ 1 > 0 and π 1 > Because skill growth is linearly related to occupation in this simple model, having µ 1 < 0 and π 1 < 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

16 (1) was 15 which can be written as j = 2α 1α 5 + α 4 α 9 + 2α 3 α 5 s j + α 6 α 9 s k + s g (2α 5 α 7 + α 8 α 9 ), 4α 2 α 5 α9 2 where j = β 0 + β 1 s j + β 2 s k + β 3 s g β 1 = 2α 3α 5 4α 2 α 5 α 2 9 β 2 = α 6 α 9 4α 2 α 5 α 2 9 β 3 = 2α 5α 7 + α 8 α 9. 4α 2 α 5 α9 2 The model implies that β 1 > 0 and the signs of β 2 and β 3 are ambiguous, depending on α 9 and other parameters. 16 The second set of implications comes from the career progression section of the model. The question is whether initial gaps in occupation choice widen, shrink, or persist perfectly over the course of a career. The answer depends on the relationship of skill growth to the worker s occupation. In the model, skill accumulation is as follows: 15 Although the one-period solution is not the true relationship if skills grow over time, it provides an approximation to motivate the empirics. The same qualitative implications hold for the dynamic solution. 16 Here, there is a one-to-one mapping between skills and task choices. In reality, worker preferences, search frictions, omitted task measures, and other factors will also contribute to workers choices of occupations. This will cause there to be variation in skills within occupation. 16

17 s g,t+1 = s g,t + ψ t s j,t+1 = s j,t + µ 0 + µ 1 j t s k,t+1 = s k,t + π 0 + π 1 k t. The experience profile ψ t of general skill is assumed to be common to all workers. Recall that the effect of general skill on occupation choice is ambiguous, so this means that the way tasks change with experience if general skill is growing is also not clear. If skill growth is positively related to occupation (µ 1 > 0 and π 1 > 0), then initial gaps will widen with experience. If µ 1 < 0 and π 1 < 0, then initial gaps will shrink. If µ 1 = π 1 = 0, then initial gaps persist perfectly. 3 Data To evaluate the implications of the model, I require data with a rich set of worker skill measures and individual career trajectories, as well as data on occupation content. I use the NLSY for the worker information and O*Net for the occupation information. 3.1 NLSY79 and NLSY97 The NLSY79 and NLSY97 are nationally representative panel surveys whose respondents were aged 14 to 22 and 12 to 16, respectively, at the start of the surveys and have been followed through the present. The NLSY is ideal for this project for two reasons. The first reason is its panel structure; the NLSY79 covers several decades of workers careers, while the NLSY97 covers the early-career outcomes of its respondents. In each survey year, workers provide information on three-digit census occupation. 17 The second key advantage of the NLSY is the inclusion of the Armed Services Vocational Aptitude Battery (ASVAB) tests, which were taken by NLSY79 respondents in 17 The NLSY97 respondents have been interviewed annually since The NLSY79 respondents were interviewed annually from 1979 to 1994 and biennially since

18 1981 and NLSY97 respondents in 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. restrict most of my analysis to workers who took the ASVAB before entering the labor market, which includes about two-thirds of the NLSY79 and almost all of the NLSY97. For these workers, the ASVAB scores can be interpreted as pre-labor market skills. While the NLSY79 alone would be sufficient for answering my research questions, my analysis is enhanced by including the NLSY97. The NLSY97 respondents are younger on average at the time of the ASVAB tests, and almost all of these workers take the tests before entering the labor market. This adds to my sample size for analysis of initial occupations and helps produce a more balanced sample. 18 The disadvantage of the NLSY97 is that it only follows workers through the early part of their careers. To estimate longer career trajectories, I also need the NLSY79. The ASVAB was developed by the United States military in 1968 and was adopted by all U.S. military branches in 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. 19 I Studies from within the military have shown that the relevant ASVAB score categories predict performance in their associated occupations (Sims and Hiatt (2001), Welsh and Kucinkas (1990)). I use the ASVAB scores to analyze the sorting patterns of civilian workers into oc- 18 Restricting the NLSY79 to workers who entered the labor market after taking the ASVAB produces a sample weighted toward more educated workers. 19 A complete list of military occupation requirements is available at 18

19 cupations. Given the military s use of these tests, this is a natural use of the data in the NLSY. Each military branch combines the scores in different ways to assign workers to occupations, so I create my own four composite categories: math, verbal, 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. 20 I also utilize a self-reported measure of sociability as a measure of interpersonal skill. NLSY79 respondents were asked in the 1985 survey to rate their own sociability, with four possible answers. Because sociability is not the same thing as interpersonal skill, I will be cautious in interpreting the results using this measure. 21 This gives me a five-dimensional specific skill vector: math, verbal, mechanical, science, and interpersonal skill. I will use years of education as my primary measure of general skill. 22 Panel A of Appendix Table 1 shows the correlation matrix of the six skill measures. The ASVAB scores are all positively correlated with education, suggesting that they contain information about general skill as well as specific skill. In regressions to evaluate the relationships of skills to tasks, the model suggests that I should control for general skill and all specific skills. The coefficient on a test score in that regression is the effect of the test score holding education fixed. I interpret this as the effect of the specific skill, holding constant general skill. I consider observations only after the worker has made a full transition to the labor market, which I define as being out of school for two consecutive interview rounds and 20 Results are similar when electronics information is included in the mechanical composite rather than the science composite. 21 Level of sociability, even if measured accurately, is not the same as interpersonal skill for a variety of reasons. The possible answers are also problematic and may convey value judgments; only 1.5 percent of respondents say they are extremely shy. Unfortunately, no comparable measure is available in the NLSY97. For all NLSY97 respondents, I set interpersonal skill equal to the mean value from the NLSY Education likely contains information about both general skill and specific skills, depending on what these workers chose to study in school. Appendix C provides a model justifying the use of education as a measure of general skill. 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. 19

20 being employed in the first of those two years. I define experience as years since the transition to the labor market began. 23 I exclude observations while workers are still in school, because the model implies that the only source of skill growth once a career begins is from the occupation. If a worker is accumulating skill in school, I consider those pre-market skills. I exclude from most of my analysis workers who transitioned to the labor market in 1981 or earlier (for NLSY79) and 1999 or earlier (for NLSY97), because these are the years the respondents took the ASVAB tests. This eliminates about one-third of the NLSY79 and about one-tenth of the NLSY97. A small number of respondents without valid ASVAB scores are dropped. I also drop the military subsample of the NLSY79. I use data from 1982 to 2010 in the NLSY79 and 2000 to 2010 in the NLSY97. Summary statistics for the NLSY79 and NLSY97 are shown in Table 1. Because I only observe the NLSY97 respondents for a few years, and the respondents with high education for even fewer years, my NLSY97 observations have lower experience and education on average. All test scores and the interpersonal skill measure are standardized separately by quarter-year of birth to adjust for both age and potential education at the time of taking the test, as suggested by Cascio and Lewis (2006) What do ASVAB scores measure? NLSY respondents took the ASVAB tests between ages 14 and 24. The tests represent the worker s skills at the time of the test, which include, among other things, inherited and innate ability, parental investments, and educational inputs and choices. Some of the inputs into ASVAB scores may reflect choices made by the worker, such as which high school courses he took, which college major he chose, and which occupation he entered or planned to enter. I cannot separate the effects of innate ability from the effects of parental investments or a worker s pre-test choices and preferences. Figures 1 and 2 display the distributions of ASVAB scores in my four composite subjects separately for men and women and for whites, blacks, and Hispanics (the dahsed 23 This definition of labor market transition is similar to those used by Farber and Gibbons (1996) and Schönberg (2007). Results are similar with different definitions. About 5% of workers return to school after making this transition. I keep counting their experience even when they have returned to school. 20

21 vertical lines denote the mean for each group). There are substantial racial and ethnic differences in ASVAB scores, with whites scoring highest on all four measures. Neal and Johnson (1996) find that AFQT differences between blacks and whites can account for much of the race gap in wages. They emphasize, however, that this does not imply that there are innate differences between blacks and whites. Rather, the test score gaps may be influenced the many factors listed above as well as (rational) expectations of future labor market discrimination. There are also ASVAB score differences by gender, as seen in Figure 1. The math and verbal scores are similar for men and women, with men scoring slightly higher in math and women scoring slightly higher in verbal. Altonji and Blank (1999) and others have noted that including AFQT cannot explain much of the wage gap between men and women. 24 However, men score significantly higher on the mechanical and verbal components of the ASVAB. I will return to this in section 5.1 as an application of the occupation choice framework, but it is worth noting here that these gender gaps in ASVAB scores may also be the product of discrimination, parental expectations and investments, and expectations of future discrimination. They should not be taken as innate ability differences. Evidence from Fryer and Levitt (2010) suggests that gender differences in math test scores widen as students spend more time in school, suggesting a role for factors other than innate ability in opening these gaps. While I do not find large differences in math scores here, the same principle may apply for the other tests. One useful check is to measure the gender gaps in test scores for the sample of NLSY respondents who took the tests before age 19. This eliminates the effects of college investments. For instance, boys are more likely to study science in college than girls; if this is driving the test score differences by gender, then the gender gaps in scores will be smaller for the age-restricted sample. In fact, the gender test score gaps are 80-90% as large for the younger test-takers as they are for the full sample. The vast majority of the gender gap in scores, then, is being driven by pre-college-age factors. This certainly does not rule out educational investments differing by gender, but it does suggest that these 24 To my knowledge, no paper has attempted to explain occupational differences between men and women using the AFQT. 21

22 investments must be occurring earlier than college. 3.2 O*Net I also require data on tasks required in each occupation. For this, I use O*Net, the Department of Labor s successor to the Dictionary of Occupational Titles. It contains detailed information on dozens of activities, skills, knowledge, and abilities used in each occupation. I call these measures tasks. A total of 159 tasks are rated for each occupation. It is useful for my purposes to summarize the data by a smaller number of factors. I require occupation-level 25 measures of math, verbal, mechanical, science, and interpersonal tasks to match the worker skill data from the NLSY. I choose a set of tasks for each category (based on their descriptions given by O*Net), and for each set of tasks, I extract a single factor using principal component analysis I am able to categorize 26 of the 159 task measures in one of my five skill categories. The remaining task information is not used. The measures I use and their descriptions from O*Net are in Appendix B. I standardize my five composite task measures to be mean 0 and variance 1, weighting by employment in the combined 1980 and 1990 decennial censuses. Table 2 provides the composite task measures for a selected set of occupations, in standard deviation units. 28 The first five occupations listed are the highest-scoring in each category: mathematicians for math, writers and authors for verbal, and so on. 25 Occupation-level task measures should be thought of as averages for that occupation. Using workerlevel data, Autor and Handel (2013) show that there is substantial variation in task performance within occupation. 26 Each task gives an importance and level measure; I use the importance measure, which gives a more intuitive ranking of occupations. Results are generally not sensitive to this choice, as the importance and level measures are highly correlated. 27 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, fine motor skills, etc. 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. 28 O*Net measures are at the level of SOC codes, while the NSLY occupations are at the 3-digit Census code level. I crosswalk the two using the mapping provided by Ruggles et al. (2010). 22

23 Appendix Table 2 shows the correlations between each task and an occupational earnings measure, which is the occupation fixed effect from a regression in the March CPS of log earnings on worker characteristics and occupation dummies. 29 Math and verbal tasks are most strongly correlated with occupational earnings, with science and interpersonal also positively correlated with occupational earnings. Mechanical tasks are slightly negatively correlated with occupational earnings. 30 Panel B of Appendix Table 1 shows the correlation matrices for occupation tasks. Math, verbal, and interpersonal tasks are positively correlated with each other, while all of these are negatively correlated with mechanical tasks. Mechanical and science tasks are highly positively correlated in occupations. 4 Empirical implementation There are two primary questions to analyze: the relationship of skills to initial occupation and how these relationships change with experience (career progression). For initial occupation choice, I will regress each of the five task measures (math, verbal, mechanical, science, and interpersonal) for worker i in an occupation using tasks j and k on all four test scores, the interpersonal skill measure, and education, restricting to early-career observations. 31 The regression equation is j it = λ 0 + λ 1 s ij + Λ 2 S ik + λ 3 educ i + ν t + ɛ it 29 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 full-time and to years 1980 to These correlations are not the true return to the task, because workers may select into occupations based on unobservable characteristics. When I regress the occupational earnings measure on the task measures, the coefficient on mechanical tasks is positive but small and insignificant. 31 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. An alternative would be to use a wage-weighted sum of the five tasks, which would put more weight on math and verbal tasks. Here I use the sum for simplicity. 23