The Effects of High School Career and Technical Educationfor Non-College Bound Students

I present a dynamic structural model of individual
choice regarding high school education curricula, post-secondary
education attainment, and early labor market opportunities. I
estimate the model to investigate the returns to education from
different types of U.S. high school curricula, with a particular
focus on career and technical education (CTE) for non-college bound
students. I estimate the model using panel data on students’ high
school course selection and labor market outcomes from the
Education Longitudinal Study of 2002, and I account for high school
curriculum self-selection by including instruments in the model for
high school CTE and academic opportunities along with local labor
market controls. The estimates suggest that, relative to general
education courses, trade CTE courses improve a non-college bound
student’s later labor market wages and chance of being employed in
a skilled occupation, while business CTE courses improve wages in
low-wage / high-non-pecuniary utility occupations. In addition, the
estimates suggest that increased CTE opportunities decrease a
non-college bound student’s propensity to drop out of high school
but also that CTE courses decrease a high school graduate’s
likelihood to pursue a post-secondary education degree. Policy
simulations suggest that incorporating vocational certification
into high school CTE curricula would cause more students to take
CTE courses and improve their labor market outcomes and that
instituting a German-style high school tracking system in the
United States would improve the education and labor market outcomes
of high school graduates at the expense of their non-pecuniary
utility in high school. Policy simulations also suggest that
providing free tuition to community college would cause more
students to take general education courses in high school, increase
graduation from community colleges, slightly increase graduation
from four-year colleges and universities, and slightly increase
average wages in the population.


Introduction
In 2014, 32% of U.S. high school graduating seniors did not attend any postsecondary institutions following graduation (Bureau of Labor Statistics, 2015). For many non-college bound students, taking career and technical education (CTE) courses in high school, which prepare them for trade and business careers, may be preferable to concentrating solely on general education courses. 2 An important question is which type of high school education is most advantageous for these students. Learning particular labor market skills while attending high school may improve the ability of these students to find well-paying jobs after graduation. Alternatively, these students may be better served over their lifetimes by learning a wide range of non-honors English, math, and science courses in high school and waiting to learn job-specific skills after graduation in the labor market.
There is disagreement among researchers and policy makers about the merits of high school career and technical education. 3 Some researchers and policy makers see high school CTE as an alternative to college which helps students find well-paying careers, while others see high school CTE as a system that limits students' future post-secondary education and labor market options. A third set of policy makers see high school CTE as a system that can prepare students to attend post-secondary education institutions as well as prepare them to enter the labor market. Partially due to this lack of consensus, high school education policy has favored an expansion of academic and general education curricula alongside a reduction in CTE curricula over the last 30 years, which has caused the number of high school students in the United States concentrating in a vocational field to fall from one-third to one-fifth since 1982 (U.S. Department of Education, 2013).
However, the Council of Economic Advisors (2010) has recently projected faster growing labor market demand for individuals with technical college degrees and specific training than for those with full university degrees. Little empirical research has been conducted on the benefits and drawbacks of high school CTE, and there remains general disagreement 2 The terms "Career and Technical Education" and "Vocational Education" are used synonymously by different sets of policy makers and researchers throughout the field and literature. I use the terms synonymously throughout this paper. 3 For a discussion of these disagreements, see Silverburg et al. (2004), Bozick and Dalton (2013), Levesque et al. (2008) among researchers about its effects, as discussed in Section 2 below.
In addition, the percentage of students who drop out of high school is sizable as is the percentage of students who begin but never complete a post-secondary education (PSE) degree. Specifically, 10% of the potential high school class of 2012 had not received a high school diploma or General Educational Development (GED) certificate by age 21 (Flood et al., 2015). 4 As well, only 29% of students who began PSE certificate / associate degree programs in 2009 had completed them in three years or less, and only 59% of students who began PSE bachelor's degree programs in 2006 had completed them in six years or less (National Center for Education Statistics, 2015). These sizable attrition rates motivate three additional questions. The first is how taking high school CTE affects the labor market outcomes of high school dropouts and students who begin but never complete PSE degrees.
The second is how the availability of high school CTE affects students' propensity to drop out of high school, and the third is how taking high school CTE affects students' propensity to complete PSE degrees.
I contribute to the literature by providing the most thorough empirical analysis of the returns of different types of high school education for different types of students to date. I estimate how different types of high school education curricula impact students' PSE attainment, later-life wages, probability of employment in a skilled occupation (as opposed to being unemployed or working in a minimum wage job), and probability of dropping out of high school. To evaluate these effects, I construct and estimate a comprehensive yet tractable dynamic structural model of high school education, post-secondary education, and labor market decisions, and I account for high school curriculum self-selection by including high school vocational and academic opportunity instruments at each student's school along with local labor market controls. Finally, I use the model to conduct policy 4 To describe the high school dropout rate, the literature usually uses a combination of two statistics: the graduation rate (percentage of students who graduate on time with a regular diploma, 81% in 2012) and the status dropout rate (the percentage of individuals ages 16-24 who are not enrolled in school and have not earned a high school degree or equivalent, 7% in 2012) (National Center for Education Statistics, 2015). Alternatively, I describe the high school dropout rate as the percentage of 21 year olds who have not earned a high school degree or equivalent, because 21 is the age at which a U.S. high school student is no longer allowed to attend high school if she has not yet graduated (the age varies slightly across states as discussed in section 3.1). simulations. The parameter estimates from the 2SLS regressions indicate that, relative to general education courses, trade vocational courses improve a student's later labor market wages and chance of being employed in a skilled occupation while business vocational courses decrease a student's wages but have little effect on employment. Structural estimates support these findings but suggest that the lower wages associated with business vocational courses are driven by occupation composition effects and occupational selection.

The model, described in detail in
Specifically, concentrating in a business vocational curriculum improves wages in lowwage / high-non-pecuniary utility occupations, incentivizing business vocational concentrators to choose low-wage / high-non-pecuniary utility occupations. The structural parameters also show that the positive returns to trade vocational education are generally confined to skilled manual labor occupations and the positive returns to business vocational education are generally confined to skilled non-manual labor occupations. Individuals who complete trade and business high school curricula are more likely to work in skilled manual labor and skilled non-manual labor occupations (respectively) than to work in unskilled occupations, relative to individuals who complete a general education high school curriculum. Next, the structural estimates suggest that concentrating in a trade or business vocational field slightly decreases the propensity to pursue a PSE degree after high school relative to concentrating in a general education field. In addition, the estimates show that an increased availability of vocational course offerings and vocational opportunities decreases a student's propensity to drop out of high school. Finally, the estimates suggest that, after I allow for two types of unobserved heterogeneity in the population, individuals in the population can be split between those who will always graduate from high school (two-thirds of the population) and those who are at high risk of dropping out of high school (one-third of the population). The estimates show that individuals who are at high risk of dropping out of high school are also less likely to attend PSE institutions, less likely to be employed, and (conditional on employment) less likely to be employed in skilled occupations. The results imply that the effects of high school vocational education are concentrated among the one-third of the population that is at high risk of dropping out of high school and of experiencing adverse labor market outcomes.
I conduct five policy simulations using the structural model and estimates, which I discuss in Section 7. First, I simulate the effect of requiring vocational curricula to be taught at every high school nationwide. This simulation causes an additional 4.9% of high school students to concentrate in vocational education curricula but has very minor effects on PSE and labor market outcomes. Second, I simulate the effect of removing vocational course offerings and opportunities nationwide. This simulation causes 3.2% of students who would have concentrated in vocational education curricula to instead concentrate in non-vocational curricula but, similar to the first simulation, has very minor effects on PSE and labor market outcomes. Third, I simulate the effect of incorporating vocational certification directly into high school vocational curricula. 5 The simulation causes an additional 2.9% of U.S. high school students to take vocational courses. The simulation also predicts an increase in the number of individuals working in skilled manual labor and skilled non-manual labor occupations, a decrease in the number of individuals working in unskilled occupations, and an increase in average wages and average welfare across the population.
Fourth, I simulate the effects of instituting a German-style high school tracking system in the United States, which divides students into vocational, general education, and academic tracks when they enter secondary school based on their standardized test scores and for which students on the vocational track receive vocational certification in addition to a high school diploma. The simulation predicts that more students graduate in both academic and vocational fields as a greater percentage of students are forced into these fields and away from the general education track. However, restricting high school options also causes more students to drop out of high school and instead pursue GEDs. The additional students on the academic track each have a higher propensity to pursue bachelor's degrees, the additional GED completers each have a lower propensity to pursue bachelor's degrees, and the additional students on the vocational track each receive vocational certificates with graduation. For individuals who graduate from high school, the additional PSE degrees and high school academic and vocational degrees increase average wages and increase the likelihood of being employed, while individuals who drop out of high school have lower wages and a lower likelihood of being employed. The simulation shows that, for a high school graduate, these later labor market benefits come at the cost of the individual's non-pecuniary utility in high school, as she does not enjoy 5 Vocational certification is historically pursued after high school graduation and is needed to work in various vocational occupations. The number of high school vocational programs that confer vocational certification has dramatically increased since 2006 (two years after the students in the ELS:2002 sample graduated high school), largely due to the Carl D. Perkins Career and Technical Education Act of 2006 (U.S. Department of Education, 2013). the academic and vocational courses she is forced to take as much as she would have enjoyed the general education courses she would have taken had they been available.
Finally, I simulate the effects of free community college for all United States high school graduates, which was recently proposed by President Barack Obama and incorporated into the education policy platforms of Bernie Sanders and Hillary Clinton (Obama, 2015;Sanders, 2016;Clinton, 2016). I find that, under this policy, more individuals complete associate degrees, more individuals pursue general education courses in high school, and a few more individuals complete bachelor's degrees. Average wages slightly increase, largely driven by the increase in bachelor's degree attainment, and average utility in the population increases, particularly prior to entering the labor market.
However, these utility gains do not offset the costs of the policy proposal (under conservative welfare assumptions).

Literature Review
The question of the effects of different types of high school curricula has not been adequately addressed in the previous literature. The studies that have been conducted in the past have largely suffered from self-selection issues which bias their results. These self-selection issues are caused by each student endogenously choosing her own high school curriculum. As students get to choose which classes they take in high school, students with different unobserved characteristics (e.g., motivation and ability in a particular high school field) may self-select into different types of classes. If these unobserved characteristics also affect labor market outcomes, such as wages and employment prospects, a researcher cannot determine whether differences in students' labor market outcomes were caused by students having taken different classes or by the unobserved factors that motivated the students to take different classes in the first place.
Without controlling for endogenous self-selection, a researcher may conclude that concentrating in a particular high school field increases later life wages when, in reality, the choice to concentrate in that field and the higher later life wages are both affected by the student's unobserved characteristics. Not addressing this self-selection issue biases the results of non-causal studies comparing the effects of different high school education curricula.
A majority of previous studies have not adequately controlled or instrumented for endogenous high school curriculum selection. In addition, they have reached contradictory conclusions using data from the same data sets (The National Longitudinal Study of the High School Class of 1972 (NLS-72), High School and Beyond (HS&B), and The National Education Longitudinal Study of 1988 (NELS:88)) due to different choices of empirical specifications. Meyer and Wise (1982), Stromback (2010), and Davis and Obenauf (2011) found no significant effect of high school CTE training on early labor force experiences, while Arum and Shavit (1995), Mane (1999), and Bishop and Mane (2004) found that taking CTE courses significantly improved non-college bound students' wages and employment chances. I briefly discuss the differences in empirical strategies across these studies, which drive their contradictory conclusions, below. Mane (1999), Bishop and Mane (2004), and Davis and Obenauf (2011) used variations of linear regression models with different specifications of explanatory and dependent variables. Mane (1999) used the total number of academic courses and total number of vocational courses completed by each student as his explanatory variables along with quadratic terms for how the number of academic and vocational courses completed by each student varied from the average across the sample. He also controlled for college attendance but did not include any instruments for endogenous high school curricula selection. Bishop and Mane (2004) split high school curriculum into five categories and ran nine different linear regressions on different wage and employment dependent variables.
They controlled for college attendance and included two high school vocational characteristic control variables to control for high school curricula self-selection: whether the school was a vocational school and the percentage of full-time faculty who were vocational teachers. Davis and Obenauf (2011) ran a linear regression of wages on high school curriculum after splitting curriculum into three mutually exclusive categories. They included a single variable to control for high school curricula self-selection: each student's self-reported interest in high school. Meyer and Wise (1982), Aram and Shavit (1995), and Stromback (2010) used more complex estimation methods but did not attempt to control or instrument for high school curricula self-selection in any way. Meyer and Wise (1982) investigated the effects of taking different high school curricula by using maximum likelihood estimation to jointly estimate tobit regressions of weeks worked, logit regressions of school attendance, and linear equations of labor market log wages. Aram and Shavit (1995) investigated the effects of high school curricula using a multinomial logit model of occupation choice with occupation separated into five distinct occupation groups. Finally, Stromback (2010) used data from the Longitudinal Survey of Australian Youth. He estimated the effects of high school vocational education using propensity score matching of high school completion and vocational education on earnings after excluding individuals from the sample who attended college. Generally, there has been a lack of consensus about the effects of taking high school CTE throughout the literature as well as an absence of rigorous, empirical studies investigating its effects.
One additional study merits discussion. Meer (2007) used data from NELS:88 and dealt with the problem of high school curriculum self-selection using the Heckman (1979) correction in addition to including a set of high school vocational opportunity instruments.
He estimated a static model with one observation of high school education in 1992 and one observation of income in 2000 for each individual. He found that there were minor positive effects of high school CTE on later-life earnings for a particular subset of the population but that a majority of individuals in that subset were already concentrating in high school vocational curricula. My research goes beyond Meer in several dimensions: it uses education and employment data from every year available in the panel data set; it uses a student's path of choices over time to infer additional information about her unobserved heterogeneity; it estimates interaction terms between the effects of high school curriculum and post-secondary education degree attainment; and it estimates the effects of CTE education on an individual's high school dropout propensity and employment outcomes jointly with the effect on her wages. In addition, the dynamic structural model allows me to separately identify the present and future benefits of education and labor market choices (e.g., present wage and utility benefits relative to future wage and utility benefits). Finally, by estimating a dynamic structural model, I am able to conduct policy simulations.
Differences include that my model is the first to look at high school curriculum choice and that it models a broader range of lifetime choices (6-12 choices in any given period, 15 choices across an individual's lifetime) than any previous model. For example, Eckstein and Wolpin (1999) included a total of six high school education and part-time / full-time work options in their model, and Chan (2013) included a total of eight labor supply and welfare participation options in his model. In addition, my estimation methodology is the first to deal with unobserved and partially unobserved choice data in some periods for some individuals in a longitudinal data set. Instead of dropping these individuals, I simulate the state vector in every period where choice data is observed, by first simulating choice outcomes in every period where choice data is unobserved, as described in Section 5.3.

Model
An individual's schooling and work decisions are modeled using a dynamic discrete choice model. Every year, an individual chooses among mutually exclusive education and labor market options in order to maximize her lifetime utility, knowing that current education and labor market decisions affect future wages and educational opportunities.
The individual's decision each year depends on the utility she receives from her decision in the current year as well as her knowledge about how that decision will affect her in the future.
The rest of Section 3 provides details about the model. Discussion of how the data relates to the model is postponed until Section 4.

Choices
As illustrated in Figure 1, the model is structured as follows: an individual begins making choices in her first year of high school when she is 14 years old. In each period, which is one year long, she chooses among: (A) Attending high school in one of five fields: Academic, General Education, Business Vocational, Trade Vocational, or Other (agriculture, health, art, physical  (B) Working in one of five types of occupations: Professional, Skilled Non-Manual Labor, Skilled Manual Labor, Skilled Other, or Unskilled; (C) Neither working nor attending school: Not Employed. 6 Once the individual has completed four years of high school, she graduates. As soon as the individual graduates, she receives a high school diploma that reflects her aggregate curriculum across her four years of high school. 7 Denote the number of years individual i has completed in high school field k prior to the start of period t as . After completing her fourth year of high school (∑ 4), individual i's aggregate curriculum vector, , is updated to indicate the field that she chose for a plurality of the four years that she completed: If the individual devoted the same number of years to multiple fields, the most recently taken field is assigned as her aggregate high school curriculum. The student is aware of how aggregate curriculum will be assigned when she makes her high school field choice each year. Her decision is driven by the enjoyment she receives from taking classes in a particular field during the current year, her knowledge of how the choice will affect her overall high school curriculum, and her knowledge of how her overall high school curriculum will affect her future wage offers and PSE choices (discussed below).
The individual cannot drop out of high school prior to age 16 due to compulsory school attendance laws. 9 The individual cannot choose to attend high school after age 21 due to high school attendance age requirements. 10 If the individual is any age over 18 and has not yet graduated from high school, in addition to her other choices, she can choose to: (D) Complete the General Educational Development exam: GED.
After completing the GED exam, individual i's aggregate curriculum vector ( ) is updated to indicate that she earned a GED: After graduating from high school or receiving a GED, the individual can no longer choose any of the five high school education options or the GED option. Instead, in addition to working and non-employment, she can choose to: (E) Attend one of three types of post-secondary education institutions: Trade School, Community College, The individual can pursue any of the PSE degrees each year, in any order. Once an individual has attended and passed one year at a trade school, two years at a community college, or four years at a four-year university, she receives a degree from that institution and can no longer attend that type of PSE institution. Let denote the number of years individual i has completed at PSE institution type k prior to the start of period t. Her PSE graduation vector, , is constructed as 9 These laws vary slightly across states. All states set their compulsory school attendance age at either 16, 17, or 18, though many states provide some exceptions which allow students to drop out prior to reaching the compulsory school attendance age (Education Commission of the States, 2015). 10 These requirements vary slightly across states, but a majority of states set the age cutoff at 21 (29 states). A minority of states set the age cutoff at 19 (1 states), 20 (9 states), 22 (1 state), 26 (1 state), or provide no age cutoff at the state level (9 states) (Education Commission of the States, 2013). 11 Throughout this paper "trade school" refers to any vocational certificate granting PSE institution, "community college" refers to any associate degree granting PSE institution, and "four-year university" refers to any bachelor's degree granting PSE institution.
After the individual graduates from a four-year university, she can choose among only work options and the "not employed" option. That is, an individual who receives her bachelor's degree cannot choose to attend a community college at a future date to pursue an associate degree. 12 The student is aware of these PSE institution graduation rules when making her choice each year. 13 Overall, there are 15 total options available to a person over her lifetime: five high school education fields, one GED exam, five occupations, three types of PSE institutions, and the not employed option. 14 The individual can choose among education and labor market options until she turns 35, after which she remains in her most recently chosen occupation for the rest of her career. This assumption conforms with labor market evidence that individuals seldom change occupations over the second half of their careers (e.g., Neal, 1999) and follows the treatment of future utility used in the previous literature (e.g., Berkovec andStern, 1991, andFrancesconi, 2002). Once the individual turns 65, she retires. Following retirement, all individuals receive the same amount of utility which is independent of previous choices. 15 12 This assumption is made to simplify the choice set available to bachelor's degree completers. Only 0.2% of individuals in the data set attended a two-year community college or a one-year trade school after attaining a bachelor's degree. 13 Approximately 20% of individuals who enroll in a two-year community college eventually transfer to a four-year university (Hossler et al., 2012). The amount of community college credit that is transferable varies widely from 0% to 100%, with an average of around 70% among transferees, which takes into account that many transfer credits do not give specific course credit towards graduation (Monaghan and Attewell, 2014). Potential future work involves expanding the model to allow community college credit to transfer to fouryear universities with a certain probability, realized after community college courses are taken. Note that I currently recode community college transfers who attain bachelor's degrees as having attended four-year universities for four years. 14 Marriage and child birth choices are left out of the model to avoid another level of model complexity and to preserve estimation tractability. Omitting child birth may add additional self-selection bias to the model if individuals who plan to have children choose specific high school concentrations and choose not to participate in the labor market. Similar to other high school curriculum self-selection bias in the model, this bias is dealt with by including instruments for high school curriculum choice and by estimating the distribution of unobserved heterogeneity in the population, as discussed in Section 5.5. 15 As an individual makes no decisions after age 35, expected lifetime utility after age 35 can be re-written as a single lump sum. The particular way this utility is distributed across periods after age 35 does not affect the individual's expected future utility except by changing the magnitude of this lump sum and by changing the extent to which early career educational attainment and occupation-specific human capital affect this lump sum.

Utility Function
The individual receives utility each period from both her current wage, if working, and the non-pecuniary characteristics of her current choice. Each period, the individual receives a wage offer in each of the five occupations. 16 Specifically, the wage offer for The symbol "~" denotes wage parameters and wage error terms. The vector is comprised of time-invariant characteristics of the individual, detailed in Section 3.3 below.
Vectors and are comprised of dummy variables for high school graduation curriculum and PSE institution graduation as defined in Section 3.1. As is a binary variable that takes the value of zero or one, vector is comprised of dummy variables for whether the individual completed a particular high school track as well as completed a PSE trade school degree / certification. 17 Vector is comprised of the occupation-specific human capital the individual has gained in each of the five occupations.
The error terms and ̃ are discussed later in this section. For non-occupation options, is equal to zero.
Next, the individual receives non-pecuniary utility each period from her current choice. The total utility she receives in a period is assumed to be a linear function of her wage, if working, and the non-pecuniary utility she receives from her choice. Specifically, individual i's total utility flow from choice k at time t is . ( The coefficient represents the utility value of wages relative to non-pecuniary utility. 16 I assume the individual receives a wage offer in every occupation every period with 100% certainty, an assumption which is used in a variety of other structural models (e.g., Eckstein and Wolpin, 1999). An individual who, in reality, did not receive a wage offer in an occupation in a period is represented in the model as having received an extremely low wage offer in that occupation in that period. 17 These interaction terms are included to investigate whether there is an additional benefit to wages from both concentrating in a particular vocational curriculum in high school and graduating from a one-year PSE trade school in addition to the benefits of graduating from each individually.
The vector = 0 for all non-PSE choices. 18 For PSE options, captures how the utility an individual gains from attending each type of post-secondary institution is affected by her previous high school education choice ( ). This is because her previous education choice affects whether she is accepted into colleges, her net tuition, and whether she knows other material that may help her in college, giving her more incentive to attend. All of these effects cumulatively make up . For the "Not Employed" option, is standardized to zero.
The stochastic error terms ̃ and (associated with wage offers and nonpecuniary utility, respectively) vary across individuals, across choices, and across time.
Each ̃ is distributed 0, , and each is distributed 0,1 . 19 The error terms and vary across individuals and across choices but are constant over time.
These error terms reflect the individual unobserved heterogeneity which motivates each person to make specific choices in the model conditional on her observables. 20 For example, and include the effects of an individual's unobserved motivation and ability in each education field and labor market occupation.

Individual Characteristics
The specific individual characteristics that constitute (which affects wages and non-pecuniary utility as defined in Section 3.2) vary across the 15 education and labor market options in the model. 21 Specifically, the effect of individual characteristics on wages in each occupation ( ) can be written as 18 and do not affect occupation non-pecuniary utility as I assume that the labor market returns to education are exclusively wage-related. That is, I assume that taking particular classes in high school will increase wages in each occupation but will not directly increase the non-pecuniary enjoyment of working in each occupation. 19 Error terms ̃ and are each assumed to be independent across individuals, choices, and time. The error term associated with the wage in each occupation each year, ̃ , can be thought of as a yearly wage bonus in each occupation that changes from year to year. The error term associated with the non-pecuniary utility of each choice each year, , can be thought of as stochastic randomness in an individual's life that changes her enjoyment of that choice from year to year. 20 No assumptions on the distribution of the pre-realized and need to be made. 21 Age/year variables are omitted from the model to decrease the parameter set. See Section 6.3 for a discussion of how their omission affects the estimation results.

Value Function
Define ̃ and as the vectors of all wage time-specific error terms and non- Every year an individual works in an occupation, she has a chance to gain occupation-specific human capital in that occupation ( ). Specifically, the law of motion of occupation-specific human capital in each occupation is where is a random variable distributed iid and realized at the end of period t. 23 The probability an individual gains occupation-specific human capital, , can take on five different values that depend upon the individual's highest level of educational attainment (i.e., no high school diploma or equivalent ( ), high school diploma or equivalent ( ), PSE trade certificate ( ), associate degree ( ), or bachelor's degree ( )). An individual's level of occupation-specific human capital is allowed to vary between low ( 0), medium ( 1), and high ( 2) in each occupation to reflect the discrete raises an individual receives, after controlling for inflation, in her occupation throughout her lifetime. Also, note that an individual can accumulate only up to two levels of occupation-specific human capital across all occupations ( O 2) over her lifetime, which follows the results of previous studies that have shown that individuals rarely accrue high levels of occupation-specific human capital in multiple occupations (e.g., Topel andWard, 1992, andPavan, 2010 where . The integral over ̃ corresponds to integrating over each of the normal ̃ error terms associated with wages in each of the five occupations. The derivation of * ̅ is similar to the derivation used in other dynamic discrete choice models such as Chan (2013).  Table 4.1. Second, the number of high school dropouts in the sample is lower than the population average, as discussed in Section 4.2. 26 Indicator variables for missing information are used for each variable that is missing information for some individuals in the data set (e.g., Test Score in Table 4.1). In  10% of students attended non-Catholic private schools. 29 Next, Table 4.2 provides summary statistics on the log hourly wages of sample members ( ). 30 Individuals in professional occupations received the highest log hourly wages, on average, followed by individuals in the skilled other, skilled manual labor, skilled non-manual labor, and unskilled occupations, respectively. Table 4.3 provides summary statistics about the high school vocational and academic opportunities at each student's school, the selection methods for school enrollment at each student's school, and the selection methods for high school course selection at each student's school ( and ). 31 Approximately three-fourths of students in the sample attended high schools that offered some type of vocational curriculum either on-site or at an area vocational school. 32 Approximately 10% of the students in the sample attended schools that conferred GED degrees on-site, and one-fourth of the students in the sample received free or reduced price lunches. Three-fourths of the students in the sample attended schools that admitted students principally based on the geographic location of 28 The range of the test scores was readjusted, originally from 20 to 80, to have a mean of zero and a standard deviation of one, in order to make the estimates easier to directly compare to the estimates for the other individual characteristics. The range of SES was also slightly readjusted, originally from -2 to 2, to have a mean of zero and a standard deviation of one. 29 Public is the omitted baseline school type in Table 4.1. 30 Each observation is a student-year log hourly wage. Log hourly wages are constructed by first converting all wages that were recorded over the length of the survey into real 2002 dollars. Wages are then converted into hourly wages and any hourly wages below 5 dollars an hour and above 100 dollars an hour are dropped. Nine percent of hourly wages are dropped because they were below $5 an hour, and one half of one percent of hourly wages are dropped because they were above $100 an hour. Finally, hourly wages are transformed into log hourly wages. Most wages in ELS:2002 were collected as hourly wages, although for a subset of student-year observations weekly, monthly, or yearly income was collected instead. These incomes are first converted to hourly wages based on the number of hours each individual worked per week and the number of months they worked throughout the year. For further details on hourly wage construction see Appendix D.1. 31 ELS:2002 includes a substantial number of variables about each high school's vocational offerings, academic offerings, and selection methods. I choose the particular subset of variables depicted in Table 4.3 to be indicative of the full set of high school-related variables available in ELS:2002. Changing the subset of chosen variables does not affect the 2SLS parameter estimates in Section 6.1 or their statistical significance. 32 An area vocational school is an off-grounds location where high school vocational courses are taught. Students who enroll in courses at an area vocational school bus between the area vocational school and their primary high school multiple times each week. their parents' homes. Next, the influence students had on their own course selection varied widely throughout the sample, though on average students had a large influence on their own course selection. 33 Nearly every student's high school offered academic counseling.

Summary Statistics
Finally, the average student attended a high school where, in regards to the previous year's graduating class, a large percent had enrolled in a four-year college, a relatively small percent had enrolled in a two-year college, and a relatively small percent had entered the labor market. 34 Table 4.4 provides summary statistics about the local labor market characteristics, in 2002, in the county in which the student's high school was located ( ). Data on average wages and industry employment percentages by county is from the Bureau of Economic Analysis's (BEA) regional data on Local Area Personal Income & Employment. 35 Data on county unemployment rates is from the Bureau of Labor Statistics' (BLS) Local Area Unemployment Statistics. 36 The average unemployment rate across counties was 4.2% 33 "Student Infl on Course Selection" is a discrete variable that takes the values of none (0), a little (1), moderate (2), and a lot (3). 34 "% Prev Students Attend 4yr College", "% Prev Students Attend 2yr College", and "% Prev Students Enter Labor Market" are discrete variables that take the values of none (0), 1-10% (1), 11-24% (2), 25-49% (3), 50-74% (4), and 75-100% (5). 35 Employment percentages across industries are used because employment percentages across occupations are not available at the county level. However, industry employment percentages closely match occupation employment percentages at the national level and at the MSA level (See Appendix C.2 for a detailed discussion). As such, industry employment percentages are a good approximation for occupation employment percentages. 36 Average wages are constructed as the total sum of wage and salary income in the county divided by the total amount of wage and salary employment in the county, converted from an average yearly salary into an average hourly wage and logged. The four industry categories of professional, manual labor, non-manual labor, and other are constructed by aggregating the 21 industry categories provided in the BEA Employment by Industry data file, which provides the percentage of employees in each county working in each North American Industry Classification System (NAICS) two-digit industry category in 2002. The manual labor category includes industries such as construction and manufacturing, and the non-manual labor category includes industries such as retail trade and real estate. Industry types that do not fit into the professional, manual labor, or non-manual labor categories, such as farm employment and educational services, are included in the other category, which is the omitted category. Additional details about the local labor market variable construction rules can be found in Appendix C.1.
with a fairly large variance across counties. The percent of employees working in each type of industry varied widely across counties, however, more employees worked in nonmanual labor and other industries, on average, than in professional and manual labor industries.

Choice Construction
Each student's yearly high school field choices are constructed using her high school transcript data. First, each course the student took is coded into one of five field After each individual course is mapped to a specific field, a single overall field concentration is constructed for each year of high school. Specifically, yearly field concentration is chosen as the field in which the student took a plurality of courses. 40 The tiebreaking rule favors labeling a yearly concentration as vocational as opposed to nonvocational, though very few ties occur. 41 After yearly concentrations are constructed, overall high school curriculum is determined as defined in Section 3.1. 42 Summary statistics on overall high school curricula are presented in Table 4.5. In the sample, 33% of students completed a general education curriculum, 21% of students completed an academic curriculum, and 5%, 5%, and 13% of students completed a business vocational curriculum, trade vocational curriculum, and other curriculum, respectively. Just under 7% of students in the sample did not graduate from high school by age 19. Unfortunately, this 7% number is around half the national average for high school dropouts by age 19 in 2005 (National Center for Education Statistics, 2015). Even under the strong assumption that all 300 sample members who are missing high school graduation information had not graduated high school prior to age 19, and correcting for the study's oversampling of 38 The complete mapping of CSSC codes to curriculum types is provided in Appendix A.1. 39 I separate "other" courses to restrict them from impacting the parameter estimates associated with general education, trade vocational, and business vocational high school curricula. 40 In practice the yearly curriculum construction rule is slightly more complicated than this with regard to the other and general education fields: students are considered other and general education yearly concentrators only if they took twice as many courses in the other or general education fields as courses in any academic or vocational field. The reason for this complexity is that students who are considered academic and vocational concentrators in the U.S. high school education system generally still take a few general education and alternative (art, health, physical education, etc.) courses each year in addition to their academic and vocational courses. This specification is similar to that of Meer (2007). 41 The tiebreaking order is trade vocational, business vocational, academic, other, and general education. Note that only 0.2% of student-year curricula observations had ties. Using alternative tiebreaking rules does not affect the estimation results. 42 The high school curricula outcomes I construct are very similar to outcomes constructed using alternative curriculum construction rules. For a detailed comparison of high school curricula outcomes under three alternative construction rules, see Appendix A.3.
private school students, this percentage is notably lower than the population average. 43 Thus, it appears that the ELS:2002 survey under-sampled students who were at risk of dropping out of high school, which means that my sample estimates regarding the effects of different high school curricula on high school dropout propensity may not be indicative of population estimates.
Next, ELS:2002 includes yearly information about post-secondary education enrollment and completion. See Table 4.6 for the aggregate PSE attainment rates in the 43 Note that the ELS:2002 data set provides sample weights for each wave of the survey based on which sample members' information was missing for that wave. However, the entire sample of 16,200 individuals (comprised of 16020 individuals in the baseline wave and 180 individuals retroactively added to the sample in the first follow-up wave) was meant to be nationally representative across a variety of demographic measures, with the exception of school control. As I use the entire nationally representative sample of 16,200 individuals in my analysis I do not use these sample weights. With the exception of the dropout rate percentage and school control, summary statistics in the data closely match population moments. Also, note that applying the ELS:2002 survey weights for any / each of the sample waves causes no more than a 0.5% increase in the dropout rate percentage in the sample, likely due to the fact that the weights did not include the high school dropout rate in the list of population moments used to create the weights. I am currently following up with the Department of Education to gain more insight into why the dropout rate percentage in ELS:2002 is notably lower than the population average. sample for each type of PSE institution at the time the study concluded in 2012. Slightly more than one-third of the students in the sample had graduated from a four-year university, while 9% and 8% of students in the sample had graduated from at most a trade school or community college, respectively. As shown in Table 4.6, these numbers are relatively similar to national college attendance and graduation rates during the sample period (Current Population Survey, 2012), with the exception that high school dropouts were under-sampled (see the discussion in the preceding paragraph). When constructing individual-year choices, I treat an individual who worked parttime while attending high school full-time or college full-time as having attended school and not as having worked. This simplification is made to greatly reduce the number of choices in the model and is used in previous dynamic structural models such as Keane and Wolpin (1997). However, it implies that an individual receives no utility or occupationspecific human capital from part-time work, which may slightly bias the estimation results. Using the construction rules discussed above, I assign each individual an education or labor market choice during each year of the sample period. If she was working part-time during the year she failed her coursework, she is coded as working. If she was not working part-time during the year she failed her coursework, she is coded as not employed. 46 This assumption is implied in previous structural models such as Eckstein and Wolpin (1999) and is analogous to the assumption in labor market literature that treats individuals who are fired from their job the same as individuals who quit their job. 47 Approximately 480 individuals in the sample attended a PSE masters, professional, or doctoral program. As I do not include this choice in the model, these individuals are currently treated as "missing information" during years when they attended these programs. based on job start and end dates, many of them are coded as missing or "Work Unknown Type" during these years. 48

Unobserved Heterogeneity
In order to estimate the model, I restrict each individual's unobserved heterogeneity values ( and ) to one of two possible sets in the population, (type one) and (type Define as the proportion of individuals in the population with type-one unobserved heterogeneity values. The elements of are standardized to zero, and the elements of and the value of are estimated in the model. This approach is similar to the treatment of unobserved heterogeneity used in the previous literature (e.g., Wolpin, 1997, andChan, 2013).

Likelihood Function
The parameters in the model are estimated using maximum simulated likelihood estimation. The likelihood function is constructed as described below. First, define an individual's realized log-wage offer in occupation k in period t as , define as a binary variable equal to one if is observed in the data set, and define , , , , … , , . Note that each contains at most one non-zero as I observe at most one log-wage offer in the data set for an individual each period.
Recall from Section 3.4 that each pre-period state ̅ includes the personal characteristics of the individual ( ), the unobserved heterogeneity type of the individual ( ), the previous high school and post-secondary education experience of the individual 48 Additional details about the imputation rules are provided in Appendix D.2. In addition to the observed choices described in Table 4.9, I observe information about whether some individuals never graduate from high school, never attain a GED, or never graduate from a particular kind of PSE institution. This information is used when calculating the likelihood functions of individuals with missing information as described in Sections 5.2 and 5.3 below.
( , , , ), and the previous human capital accumulation of the individual ( ).
Also, recall that each state vector includes ̅ as well as the period t utility and logwage error terms ̃ and . Define the expected value of log wages in occupation k in period t as ̅ ̃ and define an individual's residual log-wage error term associated with realized log-wage offer as Finally, define ̃ \ ̃ | ̃ as the joint density function of the log-wage error terms for every occupation except occupation k, conditional on the realized residual log-wage error term for occupation k. As each ̃ is assumed to be iid, the joint density of the unobserved ̃ 's does not depend on the value of the realized residual ̃ . That is, where is a four-by-four identity matrix corresponding to the four occupations with unobserved wages in period t.
Recall that is a function of which is a function of ̃ as defined in Section 3.4. Because the non-pecuniary error terms for each choice ( ) are distributed 0,1 , the conditional likelihood that individual i, with pre-period state ̅ , chose Note that has two effects on the likelihood function. First, when a wage is observed ( 1), the corresponding residual log-wage error term ( ̃ ) is directly inserted into the likelihood function. Second, when a wage is observed (  1), the corresponding residual log-wage error term affects the conditional joint distribution of the remaining unobserved error terms ( ̃ \ ̃ | ̃ ), which is integrated over to calculate the likelihood function. 49 Also, note that, as the pre-period state ̅ includes a particular unobserved heterogeneity type , the likelihood function ̅ , is conditional on the specific unobserved heterogeneity type in ̅ .
Every period that a log wage is observed a wage likelihood can be calculated.
Because each log-wage error term is distributed 0, , the conditional likelihood that a particular log wage was offered in occupation k in period t, given pre-period state ̅ , is Thus, the total conditional likelihood contribution for individual i in period t, given a particular pre-period state ̅ and observed wage vector , is The sample likelihood function (L) is the product of each sample member's individual likelihood contribution: , , .
Values of the parameters in the model are chosen iteratively to maximize the sample likelihood function. 52 The covariance matrix of maximum simulated likelihood estimates is standard. 53 51 For example, if an individual never graduated from high school and worked in a skilled manual labor job in every period t = 1,2,…,T, the probability that pre-period state path ̅ occurred in which no occupationspecific human capital was accumulated is ̅ = 1 . 52 Parameter values are chosen following the Berndt, Hall, Hall, and Hausman (1974) (BHHH) optimization algorithm. 53 Estimation code is available upon request. Due to secure data disclosure requirements, all parameter values are estimated on a stand-alone secure data computer.

Simulation
Integrating over the distribution of each unknown wage error term ̃ to calculate each * ̅ and ̅ , function, as described in Equations 4 and 6, respectively, is computationally burdensome. In addition, calculating the lifetime likelihood function for individual i for every possible choice path such that ∈ and every pre-period state path ̅ such that , ∈ ̅ is computationally burdensome. To simplify these calculations, simulation methods are used. , given pre-period state ̅ , is simulated as 54 Borsch- Supan and Hajivassiliou (1993) showed that 20 simulations without antithetic acceleration is a large enough number of simulations to produce consistent estimates. Geweke (1988) showed that antithetic acceleration reduces the sample size required to produce consistent estimates for an initial sample of 20 by at least a factor of four. As such, 10 simulations is a large enough number of simulations to construct consistent estimates of * and . Recall that is the set of all time periods for which the individual's choice was observed in the data set (i.e., all periods for which = 1). The conditional lifetime likelihood function for individual i is approximated as the average of 10 simulated conditional lifetime likelihoods, using antithetic acceleration: , , ,

Model Parameters
The number of parameters to estimate in the model, though sizable, is small enough to facilitate estimation. Specifically, there are 479 total parameters to estimate in the model. Finally, there are seven parameters that do not directly affect wages or non-pecuniary utility. These remaining parameters include a parameter for the relationship between wage and non-pecuniary utility ( ), a parameter for the variance of the normal wage error terms ( ), a parameter for the percentage of the population with type one unobserved heterogeneity ( , and four parameters for the probability of gaining work experience given different levels of educational attainment ( ).

Identification
Two types of identification issues merit discussion. First, I address the issue of what moments in the data identify each of the parameters in the model. Second, I address the issue of how the exogenous variation of the instruments (presented in Table 4.3) and estimation of unobserved heterogeneity deal with the bias caused by high school curriculum self-selection. To deal with the concern that local school board choices about vocational offerings may be correlated with local labor market conditions (e.g., local school boards in areas with more CTE labor market job opportunities may choose to offer more CTE programs in their high schools), I add controls for the local labor market characteristics in the county where each school is located. After controlling for the local labor market characteristics around each school, the remaining difference in CTE opportunities across schools is fully accounted for by state requirement differences and local randomness that is uncorrelated with local labor market conditions 55 A potential extension to this research involves constructing PSE instruments for the distance from an individual's high school to the nearest post-secondary trade school, community college, and four-year university following Card (1995). While these instruments were considered, they were not constructed due to the time and effort it would take to construct them for each of the 750 high schools in the sample.
(e.g., historic curriculum offerings at that school, a CTE teacher happening to live in the area, school board superintendent preferences, etc.).
Another potential endogeneity concern is that a family may choose where to live based on the location of the school that the family wants its child to attend. However, for a lower income family whose child is more likely to take general education and vocational education classes, the family's housing choice is much more likely to be motivated by the parents' job and housing situation than by the vocational programs available in the area school system, as discussed in Lareau (2011). A final concern is that, conditional on housing location, parents sometimes have an endogenous choice between multiple nearby high schools for their child to attend. I deal with this concern by including indicators for the type of each student's high school (public, non-Catholic private, Catholic) as well as an indicator for whether the high school admits students primarily based on geographic area, which is the case for 74% of the students in the sample. 56

Structural vs. Non-Structural Estimates
In Section 6 below, I estimate the parameters of various non-structural models in addition to the parameters of the structural model described in Section 3. While both types of estimation results provide insight into the educational attainment and labor market effects of career and technical education, the structural estimation strategy has a variety of advantages over the non-structural estimation strategy.
First, by estimating a structural model, I am able to separately identify the intertemporal benefits of different choices and how those choices affect present and future utility separately. A less structural model is unable to separately identify whether the benefit of making a particular choice in the current period is driven by increased utility in the current period or by increased utility flows in future periods and is unable to separately identify the specific mechanisms that cause current and future utility flows to increase. For example, by estimating a structural model, I can identify whether a student takes high 56 Further, conditional on housing location, a student in a rural area is less likely to have a choice between multiple high schools than a student in an urban area. As such, estimates for rural students in particular should not be subject to this potential school selection bias.
school vocational education because of the current period utility she derives, because of its effects on her future PSE institution utility, or because of its effects on her future wages in each occupation, as discussed in Section 5.5. Due to this identification, the parameter

Two-Stage Least Squares Estimates
First, I estimate linear models of later-life wages and employment using two-stage least squares estimation. The 2SLS regressions use data on each student's HS curriculum, PSE attainment, and wage and occupation information at the time the final survey wave was conducted in 2012.
The first-stage regression, used to construct high school curriculum predicted probabilities, is a multinomial logit regression of high school curriculum on personal characteristics ( ), local labor market characteristics ( ), and high school vocational instruments ( ). The estimates from the first-stage regression are displayed in Table 6.1; note that all estimates are relative to graduating high school in a general education curriculum. Overall, men are more likely to concentrate in a trade vocational field then women. Specifically, men receive 1.43 more utils than women from concentrating in the trade vocational curriculum relative to concentrating in the general education curriculum. Each instrument has a significant effect on the utility associated with at least one high school curriculum relative to graduating in the general education field, with the

1.63
Notes: 1) Multinomial Logit regression. Estimates are relative to graduating high school in the general education field.
3) Standard Errors (SE) are clustered at the school level. 4) Total # Observations is 15,890.

1.29
Notes: 1) Multinomial Logit regression. Estimates are relative to graduating high school in the general education field.
3) Standard Errors (SE) are clustered at the school level. 4) Total # Observations is 15,890. are more likely to pursue GEDs and are also slightly more likely to drop out of high school.
Whether schools admit students based on geographic location has little effect on curriculum choice, with the exception that students are less likely to pursue GEDs or dropout. Finally, as students' influence on course selection increases, students are more likely to take business vocational courses relative to general education courses and are less likely to pursue GEDs.   receive higher wages. Individuals from urban communities receive lower wages than individuals from suburban or rural communities, and wages tend to be higher in the west and northeast than in the south or Midwest. Finally, as average wages in a student's high school county increase, her later-life wages increase. Table 6.3 presents the estimates from two different second-stage logit regressions.
In the first, I regress whether or not an individual is employed at age 26, and, in the second, I regress whether or not an individual is employed in a skilled occupation at age 26 (relative to being employed in an unskilled occupation) conditional on being employed. These two binary variables are regressed on personal characteristics ( ), local labor market characteristics ( ), high school curriculum predicted probabilities ( from the regression in Table 6.1, and post-secondary education attainment predicted probabilities ( from a separate first-stage regression using the instruments presented in Table 4.3, Section 2. The estimates in Table 6.3, Column 1, suggest that concentrating in a business or trade vocational curriculum causes a positive but statistically insignificant increase in the chance of being employed relative to concentrating in a general education curriculum. E.g., the estimate on "Prob Business Vocational" in the "Employed" column indicates that, as the probability of graduating in a business vocational curriculum goes from zero to one (relative to graduating in a general education curriculum), the utility an individual receives from being employed increases by .74 utils. Column 1 also shows that concentrating in the other curriculum decreases the chances of being employed at age 26 and that dropping out of high school decreases the chances of being employed at age 26.
Next, the results in Table 6.3, Column 2, suggest that taking trade vocational courses increase the chances of being employed in a skilled occupation (relative to an unskilled occupation) conditional on being employed by 3.03 utils. The results also suggest that an academic high school curriculum has little effect on employment relative to a general education high school curriculum. Graduating from a four-year university greatly increases the chances of being employed later in life (by 2.33 utils), and individuals who graduate from community college are much more likely to be employed in unskilled occupations than those who do not graduate from community college. 60 Finally, individuals who attend schools in counties with high percentages of professional labor employment have higher chances than average of being employed at age 26, while individuals who attend schools in counties with high percentages of manual labor employment have lower chances than average of being employed at age 26.

Structural Estimates
Structural estimates are presented in Tables 6.4-6.7. 61 Selected structural wage and 60 Note that each of the results in Table 6.3 is robust to choosing different subsets of instruments in the first-stage regression with two exceptions: the skilled occupation parameter estimates for community college and four-year university graduation vary in significance as I run the regressions on different subsets of instruments (though the estimate on community college always has a negative sign and the estimate on four-year university always has a positive sign). 61 The remaining structural parameters are presented in Appendix F. utility parameters related to occupation choices are presented in Table 6.4. Looking vertically at each column in Section 1 provides a comparison of how each type of high school curriculum and PSE degree affects log wages in a particular occupation. First, graduation from high school in any field improves wages in four of the five occupations relative to dropping out. As expected, a business vocational curriculum has the greatest effect on log hourly wages in the skilled non-manual labor occupation (.29), while a trade vocational curriculum has the greatest effect on log hourly wages in the skilled manual labor occupation (.11), relative to any other high school curricula (for comparison, the effect of a general education curriculum on log hourly wages in the skilled manual labor occupation is .04). The large log hourly wage parameters associated with the skilled other occupation (ranging from 2.15 to 2.39), combined with the small log hourly wage constant for the skilled other occupation (-.59 relative to log hourly wage constants for the other occupations ranging from 1.30 to 1.89), imply that high school dropouts receive very low wages in the skilled other occupation relative to individuals who graduate from high school.
Finally, the negative log hourly wage parameters for high school graduation associated with the professional occupation (ranging from -.26 to -.14) imply that individuals who drop out of high school receive higher wages than individuals with only a high school degree in the professional occupation. This result is driven by the fact that few individuals in the data set work in the professional occupation without having earned a bachelor's degree and that, of those individuals, high school dropouts had slightly higher wages than individuals with any type of high school degree. The parameter estimates imply that the education wage premium in the professional occupation is almost entirely concentrated in four-year university graduation (an increase of .46 log hourly wages) as opposed to being concentrated in high school graduation.
The 2SLS regression result that a business vocational curriculum has little effect on wages relative to a general education curriculum, discussed in Section 6.1, does not appear in the structural estimates. Interestingly, the structural estimates show that this 2SLS result was driven by two factors. First, the structural estimates break up wages by occupation type. Once wages are allowed to vary across occupations, the estimates suggest that a business vocational curriculum improves log hourly wages in the skilled non-manual labor occupation (.29) more than any other high school curriculum improves log hourly wages in the skilled non-manual labor occupation. Since the skilled non-manual labor occupation has the lowest average wages of any occupation type, and a larger proportion of individuals who graduate high school in the business vocational field choose that occupation relative to individuals who graduate high school in other fields (such as general education), business vocational curriculum completers receive lower wages on average across occupations.
Second, the structural estimates answer the question of why business vocational completers choose skilled non-manual labor occupations (which provide lower average wages) more than other individuals, after controlling for observables. This choice is driven by the higher total utility (wage plus non-pecuniary utility) business vocational completers receive from the skilled non-manual labor occupation relative to other occupations.
Though wages are lower on average across the sample in the skilled non-manual labor occupation relative to other occupations, non-pecuniary utility is higher on average across the sample in the skilled non-manual labor occupation relative to other occupations (as seen by comparing the non-pecuniary utility constants in Table 6.1). Since an individual with a general education high school curriculum is more or less indifferent between different occupations after taking into account both the wage and non-pecuniary utility she receives, an individual with a business vocational high school curriculum is more likely to choose a skilled non-manual labor occupation, due to the relative increase in wages she receives in that occupation. Thus, a business vocational concentrator chooses the skilled non-manual labor occupation because of the non-pecuniary utility the occupation provides in addition to the wage premium she receives in the occupation from graduating high school with a business vocational curriculum, despite the fact that the job provides lower total wages than other occupations available to her. Similar incentives cause individuals who take trade vocational high school curricula to work in skilled manual labor occupations, individuals who take other (alternative) high school curricula to work in skilled other occupations, and individuals who take academic high school curricula to work in the professional, skilled non-manual labor, and skilled other occupations.
Next, recall that an individual's choice of whether to work in the model is driven by three factors: the wage offer she receives in each occupation in the current period, the non-pecuniary utility of each occupation in the current period, and the increase in future wages she will receive if she gains occupation-specific human capital from working in the current period. As an individual receives a wage offer in every occupation each period with 100% certainty, the effects of high school curriculum on employment and skilled employment are driven exclusively by the wage premium of each type of high school graduation curriculum in each occupation. Note that business vocational and trade vocational curricula provide higher wage returns than a general education curriculum in the professional, skilled manual labor, and skilled non-manual labor occupations. Also, note that, in the skilled other occupation, a trade vocational curriculum provides higher returns than a general education curriculum which provides higher returns than a business vocational curriculum. Finally, note that, in the unskilled occupation, a general education curriculum provides higher wage returns than either a business vocational or trade vocational curricula. Thus, by providing higher wage returns across all skilled occupations, a trade vocational curriculum conclusively increases an individual's likelihood to be employed in a skilled occupation, which confirms the 2SLS result in Table 6 Table 6.3.
Finally, graduating from a four-year university provides very high log hourly wage returns to all occupations but provides particularly high returns to the professional occupation (.46). Community college and one-year trade schools provide much smaller returns overall, with community college graduation providing slightly negative returns in the skilled manual labor, skilled non-manual labor, and unskilled occupations. Men receive higher wages than women in every occupation except the skilled non-manual labor occupation, and wages tend to increase on average as an individual's socio-economic status and test score each increase. In addition, the non-pecuniary utility of each occupation, relative to choosing not to work, also increases as an individual's socio-economic status and test score increase. Finally, gaining occupation-specific human capital in each occupation adds a large premium to log hourly wages (ranging from .71 to .83), though occupation-specific human capital gains occur infrequently over an individual's lifetime (9%-14% chance each year based on educational attainment).
Selected structural estimates regarding PSE choices are presented in Table 6.5.
Note that all estimates in Table 6 four-year universities than other demographic groups.
Selected structural estimates regarding HS choices are presented in Table 6.6.
Increased vocational offerings and opportunities, controlling for local labor market conditions, nearly all increase the utility of taking a vocational curriculum in high school.
For example, schools that offer marketing courses in high school increase the nonpecuniary utility of concentrating in the business vocational field each year by .50 utils.
Additionally, as the percent of students in the previous year's class who took academic classes increases, the non-pecuniary utility of concentrating in an academic curriculum increases by .82 utils. As well, schools that confer GEDs on-site increase the non-pecuniary utility of completing a GED degree by 2.15 utils. These estimates imply that, as the vocational and academic opportunities in high school increase, the high school dropout rate decreases, as each vocational and academic opportunity increases the utility of concentrating in a vocational or academic curriculum relative to dropping out of high school to pursue occupation choices or the not employed choice. Different vocational and academic opportunities increase the utility of concentrating in different types of high school curricula, which differentially decrease the dropout propensity for each at-risk student based on the high school curriculum they each would be most likely to concentrate in if they do not drop out of high school. Finally, women receive higher utility than men in the academic, general education, business vocational, and other high school fields. In   Notes: 1)*,**,*** denote 90%, 95%, and 99% statistical significance respectively.
3) Standard errors (SE) are calculated using the covariance of the parameter estimate scores, following Train (2003).

Academic General Ed
Business Voc Trade Voc Table 6.6: Selected HS Education Structural Parameters Other addition, individuals with a higher socio-economic status and higher test scores receive higher non-pecuniary utility from attending each high school field relative to dropping out of high school.
Lastly, Table 6.7 presents the estimates for unobserved heterogeneity. Recall that the unobserved heterogeneity parameters for the first type of individual in the population are standardized to zero. Table 6.7 presents the unobserved heterogeneity parameters for the second type of individual in the population, which is estimated to comprise 34.3% of the population. In order to evaluate individuals with the second type of unobserved heterogeneity, the estimates in Table 6.7 must be added to the constants in Tables 6.4-6.6.
Note that the constants for high school curricula in the bottom row of Table 6.5 are quite large (23.2 to 27.1 utils). These large high school curriculum constants imply that anyone who has the first type of unobserved heterogeneity (65.7% of the population) will never drop out of high school. The non-pecuniary utility of attending high school for these individuals is so high that they will always choose to attend high school for four years, no matter their other demographic characteristics. Next, note that the high school curriculum unobserved heterogeneity parameters for the second type of individual in the population, presented in Table 6.7, are negative and of a similar magnitude (-33.71 to -32.0 utils) to the constants for high school curricula. These estimates imply that, for an individual who has the second type of unobserved heterogeneity, not graduating from high school is a distinct possibility, which is driven by how the individual's other demographic characteristics affect the utility she derives from attending high school. Individuals with the second type of unobserved heterogeneity also receive lower non-pecuniary utility from working and from attending PSE institutions and are much more likely to choose to be neither working nor attending school than individuals with the first type of unobserved heterogeneity.

Model Fit
Figure 6.1 compares ELS:2002 student outcomes with simulated student outcomes, given the initial conditions of each student in the data set at age 16 and the parameter estimates discussed in Section 6.2. The aggregate simulated student outcomes closely reflect the aggregate student outcomes observed in the data. However, the structural model slightly over-predicts the number of individuals who graduate from high school in a general education curriculum, at the expense of graduating from each of the other four high school curricula. In addition, the model under-predicts the number of individuals who earn GED degrees, instead simulating that they will never graduate from high school. It also underpredicts the number of individuals who work in unskilled occupations, instead simulating 2)*,**,*** denote 90%, 95%, and 99% confidence respectively. 3) Total # Observations is 16,200.

Non-Pecuniary
Utility Wages 1) The estimate for the percentage of the population with type-two unobserved heterogeneity is 34.3%. 4) Standard errors (SE) are calculated using the covariance of the parameter estimate scores, following Train (2003). Table 6.7: Unobserved Heterogeneity Parameters 62 that they will be unemployed. Next, it under-predicts the number of individuals who obtain one-year PSE trade degrees and over-predicts the number of individuals who obtain fouryear university degrees. Finally, the model largely over-predicts the number of individuals who are still attending PSE institutions in 2012. This over-prediction, related to PSE attendance, is driven by the assumption in the model that the non-pecuniary utility from attending a PSE institution does not change over time. In reality, the non-pecuniary utility from attending a PSE institution likely decreases over time as an individual become older than their potential peers at each PSE institution. Since the non-pecuniary utility from attending college in the model remains constant as an individual ages, the model overpredicts the number of individuals that choose to attend college both during and after turning 26.

Policy Analysis
I use the structural estimates discussed in Section 6.2 to conduct four policy simulations. The results of each policy simulation are presented in Tables 7.1 and Table   7.2 relative to the results of the simulation under current policy settings presented in Section 6.3. 62 The simulated wage differences in Table 7.2 are averaged across all individuals who choose to work at age 26 in both the baseline simulation and policy simulation and whose simulated wages at age 26 differ between the baseline simulation and the policy simulation. The simulated early-life utility (i.e., realized utility between ages 16-26) and later-life utility (i.e., expected utility from ages 27+) differences in Table   7.2 are averaged across all individuals whose simulated early-life and later-life utility differed between the baseline simulation and the policy simulation.

Federal Vocational Offering Requirements
The structural estimates suggest that both business high school vocational education and trade high school vocational education are beneficial for the later-life outcomes of a subset of non-college bound students. The first policy simulation I conduct investigates ways to incentivize more students to concentrate in vocational high school curricula. Specifically, this policy simulation investigates the extent to which vocational curriculum take-up rates would increase if we increased the number and access of vocational opportunities in high school nationally.
I simulate the effects of a federal mandate requiring vocational education to be taught on-site in every high school nationwide. The results of this simulation are shown in Column 2 of Tables 7.1 and 7.2. This policy increases the percent of individuals who take high school vocational curricula by 4.8% and decreases the percent of individuals who take other types of high school curricula. This change in high school curricula choice, in turn, causes a few additional individuals to complete two-year community college degrees and a few less individuals to be working in unskilled labor occupations. Overall, however, this policy has little long-term effect on individuals' overall PSE attainment, occupation 62 Note that general equilibrium labor market effects are not taken into account in these policy simulations. The model assumes that the wages and utility for each occupation remain constant as students in the population change their labor supply decisions. This assumption may slightly bias the results, which is worth noting when drawing conclusions from these simulations.
choices, and employment chances. Table 7.2 shows that this policy slightly increases the average wages of individuals who switch their high school curricula to vocational high school curricula and increases average lifetime utility for these individuals.

Removal of Vocational Offerings
Next, I simulate the effects of removing vocational course offerings from high schools and area vocational schools nationwide, while keeping other high school course offerings and extracurricular offerings the same. Specifically, I simulate the effects of having every high school nationwide no longer offer vocational classes, marketing classes, or precisions classes on site or at an area vocational school. Note that this does not imply that vocational courses are strictly unavailable to students (students can still go out of their way to take other vocational courses or bus to other nearby locations that may offer vocational course credit); it instead implies that vocational courses are much more difficult to pursue.
The results of this simulation are shown in column 3 of tables 7.1 and 7.2. As expected, removing vocational offerings largely decreases the number of individuals who pursue high school vocational curricula. However, similar to the simulation discussed in section 7.1, this policy has little effect on individuals' PSE attainment and employment outcomes. Finally, individuals who changed their high school curricula due to the removal of vocational course offerings had lower average wages and lower average lifetime utility.
While this simulation predicts that this policy would decrease average student welfare, in order to perform a full cost-benefit analysis the decrease in average student welfare would have to be compared with the cost savings of removing vocational course offerings across schools.

Vocational Certificates in High School
The second policy simulation investigates the effects of allowing individuals to receive a vocational certification in high school when they concentrate in a vocational curricula. Historically, vocational high school education in the United States has not included industry certification exams or certificate conferral: students have had to take relevant certification exams after graduating from high school, by attending one-year PSE trade schools or taking the exams independently, in order to become certified. Over recent decades, however, the number of high school vocational programs that confer vocational certifications has begun to increase (Castellano et al., 2005)  2. This policy incentivizes many additional students to concentrate in a trade vocational curriculum in high school (2.9% of U.S. high school students), as it allows them to receive 63 Note that I am assuming that the returns to high school vocational education and one-year PSE trade degrees are driven by the knowledge a student learns and the degrees that are conferred at graduation as opposed to any signaling value the student receives from choosing to pursue each degree separately. To the extent that the latter is true, the results of this policy simulation are upwardly biased.
both a high school diploma and an industry certification concurrently. Fewer individuals graduate from a community college or a four-year university, however, because fewer individuals take academic and general education courses in high school. Finally, this policy leads to more individuals working in the skilled non-manual labor and skilled manual labor occupations and decreases the number of individuals working in the unskilled occupation or choosing not to work. Individuals' average wages increase as does their expected lifetime utility after the age of 26. Overall, the simulation predicts that incorporating vocational certifications into high school vocational curricula will have large positive effects on students' labor market outcomes.

German-Style High School Tracking
Next, I simulate the effects of the United States instituting a high school tracking system similar to the tracking system used in Germany. In Germany, students are split into three separate tracks when they enter secondary school: a vocational track (Hauptschule) which prepares students for career and technical occupations, a general education track (Realschule) which teaches students general education math, science, and English content, and an academic track (Gymnasium) which teaches students rigorous academic content and prepares them for a university education. Tracks are chosen for each student based on their abilities and grades throughout primary school and to a lesser extent student and parent preferences. By comparison, relatively little tracking occurs in the United States: most students retain a large amount of control over the high school course they take throughout their high school experiences. This policy simulation investigates how restricting U.S. students' ability to select their own high school curriculum, and pushing students onto particular tracks when they begin high school, would impact student's education and labor market outcomes. The results of this simulation are presented in Column 4 of Tables 7.1 and 7.2. By forcing students onto particular tracks, many more students graduate in academic (8.2%) and vocational curricula (11.9%) who otherwise would have chosen a general education curriculum. However, due to the restricted high school options, many more students also decide not to finish four years of high school and instead pursue GEDs (9.5%). The additional academic high school concentrators are each more likely to graduate from four- year universities while the additional GED completers are each less likely to graduate from four-year universities, leading to an overall slight decrease in the number of individuals who attain bachelor's degrees. The additional vocational concentrators each receive a vocational certificate at high school graduation, which contributes to decreasing the number of individuals in the population without any PSE credentials and causes more individuals to be employed in the skilled manual labor and skilled non-manual labor occupations. Overall, the individuals who are forced onto academic and vocational tracks, who otherwise would have concentrated in the general education field, realize better labor market outcomes as long as they finishing high school. For these students, improved labor market outcomes come at the expense of non-pecuniary utility in high school as the students would have preferred to take a general education curriculum if it had been 64 In the simulation, I allow students on any of the three tracks to attend all types of PSE institution following high school graduation. In the German system, it is more difficult for students who graduate from Realschule and Hauptschule to attend four-year universities (though not impossible) than for students who graduate from Gymnasium. A question of future work is whether to incorporate this difficulty into the policy simulation by calibrating the variables to reflect the ease / difficulty of attending college after graduating from each type of German high school. available. However, many students who are forced onto the academic and vocational tracks choose not to finish high school and instead complete GEDs, which leads to worse education and labor market outcomes for this subset of students. Cumulatively, across the population, this leads to slightly higher average labor market wages, labor market utility, and skilled employment opportunities, though benefits are concentrated among non-GED high school graduates.

Free Community College
Finally, the forth policy simulation investigates the effects of a policy that makes community college free for all United States high school graduates. In January 2015, President Barack Obama proposed a plan to make two years of community college free for all students in the United States (Obama, 2015), which has since been incorporated into the policy platform of 2016 presidential candidates Bernie Sanders and Hillary Clinton. 65 As the model takes into account education choices, labor market choices, and forward-looking behavior, an interesting question is what the model predicts the effects of this policy would be on students' high school education, PSE attainment, and labor market outcomes. While the monetary cost of community college is the same for all individuals, I assume that the non-pecuniary utility associated with this monetary cost is higher for poorer students than for richer students, due to diminishing marginal utility of wealth. As such, I allow the reduction in the non-pecuniary cost of community college to vary across individuals based on their socio-economic statuses. Specifically, I assume that the individual with the highest socio-economic status in the sample receives no non-pecuniary utility reduction in the cost of community college due to this policy, and I assume that the individual with the lowest socio-economic status in the sample receives double the average non-pecuniary utility reduction in the cost of community college due to this policy. 66 The results of this policy simulation are presented in Column 5 of Tables 7.1 and 7.2. Decreasing the cost of community college causes many more individuals to attend community college (15.3% of U.S. high school students) as well as more individuals to concentrate in general education courses in high school (1.1% of U.S. high school students) (as high school general education courses improve the non-pecuniary utility of attending community college) at the expense of taking academic courses in high school. In addition, fewer individuals drop out of high school (-0.7%) as high school graduation is required to attend community college. Next, the policy predicts that fewer individuals will graduate from four-year universities by the age of 26 (3.4%) but more individuals will be attending four-year universities at the age of 26 (2.0%). Recall that my model does not allow community college credit to transfer to four-year universities, when in reality approximately 50% of community college credit is transferable (Monaghan and Attewell, 2014) and approximately 20% of individuals who enroll in a two-year community college eventually transfer to a four-year university (Hossler et al., 2012). Under the weak assumption that this policy would not increase the 20% transfer rate, the model predicts that 20% of new community college graduates (who do not obtain four-year university degrees by age 26 in the simulation) would transfer to and graduate from four-year 66 In reality a subset of low socio-economic status individuals currently receive Pell Grants that decrease the cost of community college to close to zero. A question of future work is whether to incorporate these Pell Grants into the simulation by holding the cost of community college fixed for the subset of students in the population who are eligible to receive these grants. universities (2.1% of U.S. high school students). Combining these individuals with the individuals who later graduate from a four-year university after age 26, this policy simulation predicts that the more total individuals (0.7%) would eventually graduate with a four-year university degree.
As more individuals concentrate in high school general education and obtain community college degrees, lifetime expected utility increases. Under the assumption that no individuals transfer from community colleges to four-year universities, the simulation predicts that average wages will slightly decrease. Under the assumption that 20% of community college attendees transfer to four-year universities, the simulation predicts that average wages will slightly increase. Overall, this simulation predicts that there would be various positive education and labor market consequences from a free community college policy. Note, however, that this policy would be fairly costly. Under the assumption that low socio-economic status students receive a utility benefit worth twice the monetary cost of community college every year they attend community college, the simulation predicts that this policy would increase social welfare under either community college transfer assumption. However, under more conservative welfare assumptions, such as an assumption that all students receive a utility benefit equal to the monetary cost of community college each year they attend community college, the simulation predicts that this policy would decrease social welfare under either community college transfer assumption.

Conclusion
In conclusion, I have found that a high school trade vocational curriculum is very beneficial to a student's later labor market wages and chances of being employed in a skilled occupation relative to a general education curriculum. I have also found that a high school business vocational curriculum is only beneficial, relative to a general education curriculum, in skilled non-manual labor occupations, which provide higher non-pecuniary utility and lower wages relative to other occupations. In addition, I have found that concentrating in a vocational high school curricula modestly decreases a student's propensity to attend PSE institutions. I have also found that additional high school vocational and academic opportunities decrease a student's high school dropout propensity but decrease it differentially for different types of students. Finally, policy simulations predict that improving high school vocational education on the intensive margin (i.e, improving the value of vocational education courses by incorporating vocational certification into vocational high school curricula) will provide greater labor market benefits than improving high school vocational education on the extensive margin (i.e., increasing the number and availability of vocational opportunities). Policy simulations also predict that a German-style tracking system, that pushes more individuals to take academic and vocational courses, will improve the labor market outcomes of high school completers at the expense of their non-pecuniary utility in high school but that it will also increase the high school drop-out rate. Finally, policy simulations predict that free community college for all U.S. high school graduates will increase the number of students graduating from community college, slightly increase the number of students graduating from four-year universities, slightly increase average wages and lifetime utility, but increase utility by less than the cost of the policy (under conservative welfare assumptions).
Pertinent areas of future research include updating the model to allow students to transfer from community college to four-year universities and adding distance-to-college instruments to the model following Card (1995 450613-16, 450711, 450803, 450806, 450808, 450836, 450850, 450853, 450856, 450870-74, 450921, 451013, 451015, 451018, 451034-37, 451171-81 General Education Courses Area and Ethnic Studies (non-honors) 05**** Foreign Languages (non-honors) 16**** Letters/English (non-honors) 23**** Liberal/General Studies (non-honors) 24**** 67 Credit hours from schools that assign a different number of credit hours in a year (e.g. 12 credit hours per year) are first adjusted so that the average number of credit hours taken by a full time student at that school each year is six.
 The year is coded as a General Education yearly field concentration if the individual took 1.25 or more General Education credits AND took less than 1.25 Trade Vocational credits, took less than 1.25 Business Vocational credits, took less than 1.25 Academic credits, and took less than 2 Other Curriculum credits.
 The year is coded as an Other Curriculum yearly field concentration if the individual took 2 or more Other Curriculum credits AND took less than 1.25 Trade Vocational credits, took less than 1.25 Business Vocational credits, and took less than 1.25 Academic credits.
 The year is coded as an Other Curriculum yearly field concentration if an individual took less than 1.25 credits in each of the other four fields.  In the event of ties, the tiebreaking order is Trade Vocational, Business Vocational, Academic. 68

A.3 Alternative Curriculum Construction Rules
I investigated three alternative curriculum construction rules. The first rule defines an individual's overall curriculum as the yearly field concentration (constructed as described above) taken during her senior year. The second rule aggregates a student's classes and credit hours across all four years of high school and then chooses an overall concentration based on aggregate credit hours in each field. 69

D.2 Additional Imputation Rules
As discussed in Section 4.2, choice information is missing for many student-year observations in the data set. In addition, conflicting choice information is provided for a small number of student-year observations. See Table D When data on whether an individual attended HS / PSE full-time or part-time is missing, I code individuals as follows: 1) These interpolation rules are only used for student-years for which outcomes are unobserved in the data.
Code as working if worked more than 20 hours a week in 2001 Every year before began attending first PSE institution is coded as not attending Every year after last began attending most recent PSE institution is coded as not attending If the first year attended and most recent year attended are both at 4-yr institutions, and the years are four years apart, the two years between them are coded as attending 4-yr institutions Code as working (type unknown) if worked more than six months each year Early Graduates : Individuals that graduated early (in 2002 or 2001) are coded as attending in 2000 and 2001, and are coded as already having finished 1-2 years of high school (respectively) prior to 2000 Late Graduates : Individuals that graduated after 2003 are coded as attending in the year of graduation All years after graduation are coded as not attending Dropouts : Every year after final dropout, including final dropout year, is coded as not attending. Every year before first dropout year is coded as attending. If dropped out twice, year of return is coded as attending and year of first dropout is coded as not attending Individuals that attended a PSE institution for at least six months in a year are coded as attending that year    1) The parameter on log hourly wages (relating wage utility to non-pecuniary utility) is 1.37, with SE of (.002) .
3) Standard errors (SE) are calculated using the covariance of the parameter estimate scores, following Train (2003).