Shaun M. Dougherty - IA de Investigación especializada en el MIT

shaun m. Dougherty

Department of Public Policy

Neag of School of Education

University of Connecticut

Storrs, CT 06269

shaun.dougherty@uconn.edu

THE EFFECT OF CAREER AND TECHNICAL

EDUCATION ON HUMAN CAPITAL

ACCUMULATION: CAUSAL EVIDENCE

FROM MASSACHUSETTS

Abstracto
Earlier work demonstrates that career and technical education
(CTE) can provide long-term ﬁnancial beneﬁts to participants,
yet few have explored potential academic impacts, with none
in the era of high-stakes accountability. This paper investigates
the causal impact of participating in a specialized high school-
based CTE delivery system on high school persistence, completo-
ción, earning professional certiﬁcations, and standardized test
puntuaciones, with a focus on individuals from low-income families, a
group that is overrepresented in CTE and high school noncom-
pleters. Using administrative data from Massachusetts, I combine
ordinary least squares with a regression discontinuity design that
capitalizes on admissions data at three schools that are over-
subscribed. All estimates suggest that participation in a high-
quality CTE program boosts the probability of on-time graduation
from high school by 7 a 10 percentage points for higher income
estudiantes, and suggestively larger eﬀects for their lower-income
peers and students on the margin of being admitted to over-
subscribed schools. This work informs an understanding of the
potential impact of speciﬁc CTE program participation on the ac-
cumulation of human capital even in a high-stakes policy environ-
mento. This evidence of a productive CTE model in Massachusetts
may inform the current policy dialog related to improving career
pathways and readiness.

doi:10.1162/EDFP_a_00224

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119

Effect of Career and Technical Education

INTRODUCCIÓN

1 .
Nationwide, more than one in ﬁve high school students take four or more of their high
school courses in a career and technical education (CTE) área, and over 90 por ciento de
public high schools oﬀer students access to CTE programs (Musu-Gillette et al. 2016).
Despite high rates of participation in CTE by high-school-aged youth, relatively little is
known about what constitutes high-quality CTE and whether it allows participants to
accumulate meaningful human capital. What evidence does exist is from an era prior
to high-stakes accountability, which has potentially shifted the incentives for schools
and students to make investments away from CTE programing in favor of academic
preparation for high-stakes tests and four-year colleges.

Despite shifting educational incentives, there is a recognized need to expand the
percentage of adults with at least some college-level training. This stems from aware-
ness of the loss of routine lower-skill jobs that has occurred in the workplace over the
last two decades, and the rising wage premiums being paid to college graduates or
those with professional certiﬁcates (Goldin and Katz 2008; Huﬀ Stevens, Kurlaender,
and Grosz 2015; Xu and Trimble 2016). Rising college wage premiums notwithstand-
En g, many states and cities continue to face high dropout rates among high school stu-
abolladuras, particularly those from lower-income families (Rumberger 2011; Murnane 2013),
emphasizing the need for education policy to attend to both margins. The continued
importance of ensuring high school graduation as a minimum educational certiﬁcate
is also driven by the continued demand for nonroutine low-skilled and moderately-
skilled jobs—the types of jobs that many high school CTE participants are prepared to
llevar (Autor, Exacción, and Murnane 2003; Autor et al. 2006; Holzer, Linn, and Monthey
2013).

Although prior work has shown that students who participate in CTE secondary
school programs enjoy a wage premium over similar students who do not, the educa-
tional beneﬁts of CTE programs have been unclear (Catterall and Stern 1986; Pittman
1991; Mane 1999; Neumark and Joyce 2001; Plank 2001; Agodini and Deke 2004;
Ainsworth and Roscigno 2005; Bishop and Mane 2004, 2005; Neumark and Roth-
stein 2006; Meer 2007; Kemple and Willner 2008; Piedra, Alfeld, and Pearson 2008;
Hanushek, Woessmann, and Zhang 2011; Dalton and Bozick 2012; Página 2012; Bozick
and Dalton 2013). Además, earlier work has mainly ignored the potential eﬀects
on students from lower-income families, a group that is overrepresented in CTE and
for whom CTE may have previously been used as a dumping ground (Gamoran and
Mare 1989; Fraser 2008; Kelly and Price 2009). CTE may provide an eﬀective path-
way through secondary school for students who may not otherwise graduate from high
escuela, or provide a bridge to meaningful postsecondary education for students who
would not otherwise have continued their schooling (Cullen et al. 2013; Stange and
Kreisman, 2014). Alternativamente, CTE programs may track students into educational pro-
grams that make them less likely to complete high school or face limited employment
or schooling options in the future. De este modo, understanding the impact of CTE participation
on students’ educational outcomes is crucial to determining its place in contemporary
education policy.

Massachusetts, a state with a long history of providing CTE, presents a compelling
case to analyze. It is distinctive in the pathways it oﬀers for CTE participation, mientras
also being among the majority of states that now require a minimum passing score on

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shaun m. Dougherty

state assessments to earn a high school diploma. In addition to oﬀering CTE at com-
prehensive high schools where some of the school’s students participate in CTE, Mas-
sachusetts also has thirty-two regional vocational and technical high schools (RVTSs)
where all students participate in CTE. Descriptive evidence indicates that students at
RVTSs have improved their performance on the state accountability test, and increased
their graduation rates (Fraser 2008; CEP 2011). Hasta la fecha, sin embargo, there has been no
systematic evaluation to estimate the causal impact of these programs, nor an explo-
ration of the mechanisms that may drive any potential positive impact. Among previous
evaluations of the impact of CTE participation, all but one—a randomized experiment
(Kemple and Willner 2008)—have suﬀered from potential selection bias because re-
searchers did not know which factors led some students to participate in CTE and others
no.

In this paper I add to the small causal literature on CTE by capitalizing on several
features of the Massachusetts CTE system to provide plausibly causal impacts of CTE
participation in an RVTS. I capitalize on a known set of criteria used for selection of
students into an RVTS in Massachusetts that includes their grades, attendance, y
discipline records from middle school. Understanding how these factors underpin ad-
mission permits an evaluation that arguably suﬀers less from potential selection and
omitted variables bias (Altonji, Elder, and Taber 2005). Capitalizing on this process
and available administrative data, I ﬁrst use ordinary least squares (OLS) with ﬁxed
eﬀects for graduation cohort and town of residence to estimate the average eﬀect on
student outcomes of participating in an RVTS. I then complement state-level admin-
istrative data with actual admissions records that I obtained from three schools (no
currently collected by the state) and use a regression discontinuity (RD) design to iso-
late the impact of participating in CTE for students on the margin of being admitted
to oversubscribed RVTSs. These dual approaches complement one another, con el
OLS supporting greater external validity and approximating an average treatment eﬀect,
whereas the RD analyses have strong internal validity but represent the local average
treatment eﬀect for the marginal student in an oversubscribed school.

This paper makes several important contributions to the literature. Primero, it focuses
on whether there are diﬀerent impacts of RVTS participation for low-income students,
OMS, on average, are overrepresented in CTE and have been less likely to complete high
school or enroll in postsecondary education of any kind. Segundo, it provides some of
the ﬁrst estimates of the impact of a particular form of CTE on educational outcomes
in the era of high-stakes accountability in a state where passage of an exam is required
to earn a diploma.

I focus on high school graduation as my primary outcome of interest because it
is broadly accepted as a signal of the minimum required human capital to access
full-time employment. As an intermediate measure of persistence, I also add an indi-
cator for whether a student is still enrolled in high school in grade 11 in order to under-
stand whether any potential eﬀects on graduation are realized through stemming early
dropout. To further understand the mechanisms of any potential eﬀect I also include as
outcomes student scores on the math and English language arts (ELLA) exams in tenth
calificación, where passing scores on each are required to earn a diploma. These scores pro-
vide insight into whether general human capital is impacted by RVTS participation, o
if most eﬀects accrue through remaining in school. Finalmente, to gauge accumulation of

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121

Effect of Career and Technical Education

speciﬁc forms of human capital not assessed on the general academic exams, I include
as an outcome whether a student earns an industry-recognized certiﬁcate.

The rest of this paper is laid out as follows. En la sección 2 I provide more detail on
the context of Massachusetts’s CTE, as well as a review of the extant literature on the
impact of CTE participation in secondary school. I then describe my analytic strategies
in greater detail, report my results, and discuss my ﬁndings. I conclude with policy
recommendations and suggestions for extending this research.

2 . B AC K G RO U N D A N D C O N T E X T
Massachusetts has been providing career and technical education through its public
school system for over 100 years and has developed a system of oﬀerings quite unique
among other states’ systems. The distinct structure of the programs and the fact that 38
percent of CTE participants are eligible for free or reduced-price lunch (whereas only
acerca de 26 percent of students not participating in CTE are free or reduced-price lunch–
eligible), make it a compelling model to study. If the system of RVTSs is successful
in promoting improved graduation rates among lower-income students, it may prove
informative to policy makers as they consider methods to reduce high school dropout
rates and improve labor-market outcomes for such students.

CTE Treatment in Massachusetts
Many states structure high school CTE delivery such that students who participate in a
CTE program spend part of their day in a comprehensive high school for conventional
academic coursework and the remainder of their day in a technical career center—often
a diﬀerent building—where they engage in CTE coursework. In Massachusetts, el
structure is somewhat diﬀerent. Students can participate in CTE through two primary
canales, with about half of all participants in each: either in specialized programs em-
bedded in comprehensive, largely college-preparatory high schools, or through RVTSs
where all students participate in some form of CTE.

CTE delivery diﬀers along important dimensions for students in comprehensive
school and RVTS programs. Por ejemplo, at comprehensive high schools, students par-
ticipate in CTE coursework as part of their typical daily schedule. This means that CTE
courses are intermixed with other academic coursework, and that students in academic
classes are a mix of CTE participants and nonparticipants. A diferencia de, at RVTSs, estu-
dents alternate on a weekly basis between full-time academic coursework and full-time
work in their technical area and all students in all classes take some form of CTE.

En tono rimbombante, state graduation requirements do not diﬀer by school type, significar-
ing that students in comprehensive high schools and RVTSs must all complete four
years of English, four years of math, three years of a lab-based science, three years
of history, two years of the same foreign language, one year of an arts program, y
ﬁve additional “core” courses such as business education, salud, and/or technology
(see www.doe.mass.edu/ccr/masscore/). Taking CTE coursework in any setting can
be thought of as a substitute of CTE electives for other electives, such as additional
world language, arts classes, or electives in core academic areas that exceed mini-
mum graduation requirements. The key treatment in this paper, entonces, is the taking
of elective CTE courses in an RVTS that is structured diﬀerently than a traditional

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shaun m. Dougherty

high school, arguably changing the overall educational experience in the ways described
above.1

Access to CTE
Access to RVTSs is largely determined by the location of a student’s home (see Ap-
pendix ﬁgure A.1 for a map of school locations and aﬃliated towns). De 36 escuelas
oﬀering CTE in a setting where all students participate in some CTE program, 27 son
run as semi-independent regional school districts, 5 are run by the city school districts
where they are located (Worcester, Springﬁeld, Lynn, Holyoke, and Boston), y ahí
are two countywide and one statewide agricultural schools. In total, 323 del 353 towns
and cities in the Commonwealth are associated with a regional technical school. On
promedio, RVTSs oﬀer nearly 18 (exactly: 17.7) diﬀerent CTE programs. As required by
the Perkins IV act, students in the remaining towns have access to some form of CTE
through their comprehensive high school (though on average comprehensive schools
oﬀer fewer than 8 [exactly: 7.6]) distinct CTE programs. En algunos casos, if particular pro-
grams are not oﬀered in their school, students can apply for a tuition transfer to attend
an RVTS in another area. Approval of tuition transfers must be made by the receiv-
ing RVTS, as well as the sending home district, which is responsible for providing the
per student allocation to the RVTS. Acerca de 18 percent of all high-school-aged students
in Massachusetts participate in some form of CTE in high school, with about half of
these students participating through an RVTS and the other half participating through
a comprehensive high school.

For this paper the most salient diﬀerences between the RVTS and comprehensive
school CTE settings are that all students in an RVTS participate in some form of CTE,
and the majority of programmatic oﬀerings in RVTSs fall under what Massachusetts
designates as Chapter 74–approved programs. In order to receive additional funding
from the state, Chapter 74–approved programs must document partnerships with rep-
resentatives from organized labor and local industry leaders in the program area to
inform curricula, performance evaluation standards, and equipment purchases. Este
public–private partnership is designed to keep training relevant and to oﬀer programs
in a manner that is consistent with local labor market needs. Chapter 74–approved
programs also require adherence to program speciﬁc student–teacher ratios and space
pautas. Más que 90 percent of programs oﬀered in RVTS settings carry this desig-
nación, whereas roughly 60 percent of programs in comprehensive settings are Chapter
74-approved. These factors suggest that RVTS settings may be diﬀerent in both their
structure and quality of the programs they oﬀer.

Evidence for the Effectiveness of CTE
Históricamente, CTE has been thought of as a dumping ground for lower-achieving or un-
motivated students (Gamoran and Mare 1989; Fraser 2008; Kelly and Price 2009).
Despite such practices, prior research has highlighted a number of beneﬁts of the

I cannot exclude the possibility that schools can set their own course content as well as their own passing
thresholds for required coursework, which likely diﬀer systematically by school. Si, on average, RVTSs were
more likely to set lower passing thresholds, then using graduation as an outcome could be less valid. Si, sin embargo,
RVTSs were no more likely than another school with students of similar prior ability to adjust course passage
requirements downward, then the graduation outcome, though imperfect, would not be as biased.

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123

Effect of Career and Technical Education

programas. Por ejemplo, descriptive work by Symonds, Schwartz, and Ferguson (2011)
found that students who have access to a structured repertoire of skills and experiences
that better prepare them for the labor market make smoother transitions into the labor
force after high school. There are also numerous studies, including one randomized ex-
perimento (Kemple and Willner 2008; Página 2012), that ﬁnd students who participate in
a CTE program have higher earnings, on average, than similar students who attended a
non-CTE program (Mane 1999; Bishop and Mane 2004, 2005; Neumark and Rothstein
2006; Meer 2007; Stern, Dayton, and Raby 2010; Página 2012).

Additional research has suggested that CTE participation may also provide non-
monetary beneﬁts. Research by Kelly and Price (2009) suggests that students derive
positive psychological beneﬁts (improvements in feelings of self-worth) from the suc-
cess and engagement they experience while enrolled in CTE coursework, y eso
CTE programs may play a role in improving student eﬃcacy along with educational
and labor-market outcomes. Supporting this idea, other research has shown that feel-
ings of eﬃcacy and self-worth are important predictors of student success in school
(Finn 1989), and that many students enter high school with limited feelings of eﬃ-
cacy (Fredricks and Eccles 2002). Because eﬃcacy and self-worth inﬂuence a student’s
engagement in his learning environment, they could have an important eﬀect on a stu-
dent’s decision to remain enrolled or drop out (Finn and Rock 1997; Agodini and Deke
2004: Plank, DeLuca, and Estacion 2008; Kelly and Price 2009; Rumberger 2011).

Despite evidence that CTE participation may promote positive ﬁnancial and psy-
chological outcomes, there is no consensus on its impact on educational outcomes.
The only large-scale randomized experiment to examine the eﬀect of CTE participation
comes from the MDRC evaluation of Career Academies (Kemple and Willner 2008;
Página 2012). Although this evaluation found important long-term income beneﬁts for
those randomly oﬀered a place in a Career Academy, there were no resulting diﬀer-
ences between the treatment and control groups in terms of high school graduation
or postsecondary outcomes.2 Although these beneﬁts from CTE may be examples of
returns on speciﬁc human capital investments (Becker 2009; Lazear 2009), nosotros también
know there are potential gains from general human capital (Becker 1962, 2009) or sig-
naling (Spence 1973; Clark and Martorell 2014) by earning a high school diploma or the
equivalente (Murnane, Willett, and Tyler 2000; tyler, Murnane, and Willett 2000).

Earlier research on the impact of CTE programs was conducted using data on
cohorts of students whose educational experiences largely predated the advent of high-
stakes accountability policies, including the administration of high school exit exami-
naciones. In more recent times, the academic requirements on students have increased,
evidenced by the use of high school exit examinations and changing diploma require-
ments that extend to CTE participants. De este modo, I hypothesize that the implementation
of high-stakes testing, and in particular the use of high school exit examinations in
Massachusetts, may have changed the way schools oﬀering CTE have been expected to
operate.

My hypothesis is consistent with the ﬁndings of Stern, Dayton, and Raby (2010), como
well as those of Neumark and Rothstein (2006), suggesting the impact of CTE diﬀers

en este estudio, students in both the Career Academies and the traditional schools had high levels of school
completion and college attendance, and so any eﬀects might have been more diﬃcult to detect.

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shaun m. Dougherty

depending on the structure of the CTE program itself. This also serves as motivation
to extend the ﬁndings of the Career Academy experiment (Kemple and Willner 2008).
Career Academies housed one or two “themed” programs that students could opt into,
but not all students in a Career Academy school participated in one of these programs,
nor did all teachers (see also Stern, Dayton, and Raby 2010). Similarmente, in Massachusetts,
the two methods of delivering CTE—oﬀerings in comprehensive schools versus those
in RVTSs—may produce diﬀerent eﬀects.

3 . R E S E A R C H D E S I G N
Two Approaches
The biggest challenge to estimating the causal eﬀects of participating in CTE through
an RVTS arises because students elect to participate, and likely diﬀer from students who
make no such choice, in both observed and unobserved ways at the time of enrollment
(Heckman 1979; Imbens and Wooldridge 2009). I deal with the self-selection problem
by using two approaches: (1) OLS with ﬁxed eﬀects for town of residence, graduation
grupo, and area of technical study (or occupational cluster; p.ej., culinary arts, electri-
California), y (2) an RD strategy in which I capitalize on a natural experiment, generated by
using a quantitative ranking process and exogenous cutoﬀ to admit students to over-
subscribed schools.3

Each approach has strengths and weaknesses, particularly in relation to internal
and external validity (Campbell 1957). Por ejemplo, my RD strategy has weaker ex-
ternal validity, because it applies only to those students on the margin of being ad-
mitted to an oversubscribed RVTS in the three schools for which I have data, pero el
ensuing causal inferences have much stronger internal validity. Por el contrario, my OLS
approach has stronger external validity because it estimates the eﬀects of CTE par-
ticipation for a larger group of students in Massachusetts, but it has weaker internal
validity.

Dataset and Sample
I use data from the comprehensive Student Information Management System provided
by the Massachusetts Department of Elementary and Secondary Education, for the aca-
demic years spanning fall of 2001 through spring 2015. These fourteen cohorts include
encima 500,000 students in grades 1 a través de 12, who are followed longitudinally for as
long as they remain in the Massachusetts public schools. For my OLS analysis, I include
students who, if they had graduated from high school “on time,” would have done so in
the spring years of 2008 a través de 2015 (aproximadamente 420,000 estudiantes). My sample
does not include students who are eligible to take an alternative assessment based on
their disability status.

For my RD analyses, I supplement the Student Information Management Sys-
tem with student-level, school-speciﬁc application and admissions records from three
escuelas. These schools have been oversubscribed for at least three years during the

3. Admissions criteria are known for RVTSs and so in the Appendix I also include a set of matching estimates
as a point of comparison with OLS. Though eﬀects are slightly smaller, the substantive conclusions are not
changed. Por lo tanto, OLS is preferred based on its requiring less methodological exposition and based on the
ﬁndings of Altonji, Elder, and Taber (2005).

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125

Effect of Career and Technical Education

Mesa 1. Summary Statistics

No CTE
(1)

Comprehensive CTE
(2)

RVTS
(3)

Grupo A: Control S

Male

asiático

Negro

Latino/a

Blanco

Lower income

Identified disability

English learner

Calificación 8 in-school suspensions

Calificación 8 out-of-school suspensions

MCAS math 8th grade

MCAS math 10th grade

4-year graduation rate

5-year graduation rate

0.496

0.053

0.051

0.084

0.843

0.197

0.147

0.043

0.008

0.012

0.198

0.194

0.815

0.828

0.585

0.045

0.088

0.138

0.767

0.375

0.22

0.074

0.022

0.016
−0.267
−0.264
0.739

0.764

Grupo B: CTE Exposure and Credentials

Years in CTE

Years in RVTS

Chapter 74 certificate

Private certificate

Non—Chapter 74 certificate

IT credential

Health credential

Engineering credential

norte

0.199

0.014

0.002

0.004

0.001

0.002

0.003

2.614

0.051

0.025

0.042

0.003

0.021

0.034

0.066

0.579

0.031

0.057

0.163

0.824

0.372

0.269

0.068

0.005

0.006
−0.357
−0.358
0.847

0.865

3.204

3.726

0.047

0.269

0.046

0.087

0.153

342,173

31,727

43,235

Notas: Mean values of key variables are shown for all students in the 2008—14 cohorts.
Inclusion in a column is defined by a student’s initial status in grade 9. CTE: career and
technical education; IT: information technology; MCAS: Massachusetts Comprehensive
Assessment System; RVTS: regional vocational and technical high school.

last decade and were forced to admit fewer students than had applied. Though nearly
thirteen schools are oversubscribed, most do not maintain historical records of their
admissions data. Además, several schools have been oversubscribed for only a few
years and do not yet have outcome data for their students. My RD sample includes over
4,000 students from three participating RVTSs, with about 2,000 of those students
just above, or just below, the admissions cutoﬀ.

Estadísticas descriptivas
En general, students who participate in any form of CTE tend to diﬀer from their non-
CTE counterparts. En mesa 1, I compare descriptive statistics pertaining to student de-
mographics and middle school characteristics, exposure to CTE, and CTE credential
attainment for students in three educational settings: non-CTE programs, CTE pro-
grams in comprehensive high schools, and CTE in RVTSs (the focal treatment group
in this study)—these correspond to columns 1 a través de 3, respectivamente. In each of the
three columns, membership is determined by a student’s status in grade 9.

126

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shaun m. Dougherty

Students in either CTE setting are less academically accomplished (measured by
resultados de las pruebas), and are more likely to be male, eligible for free or reduced-price lunch, y
to have an identiﬁed disability. Especially noteworthy is that students in comprehensive
CTE and RVTSs appear similar on nearly all observables except for their mean prob-
abilities for on-time graduation. Also noteworthy is that most students who attend an
RVTS in grade 9 appear to stay for all four years of high school, and very few students
in CTE programs in comprehensive high schools ever enroll in an RVTS. Graduation
rates are descriptively higher for RVTS students than non-CTE participants, and lower
among those in CTE programs in comprehensive high schools. Students in RVTSs are
also more likely to earn industry-recognized credentials, especially in higher-wage areas
like information technology, health sciences, and engineering.

Measures
My primary outcome of interest is a dichotomous indicator (GRAD4) of whether a stu-
dent graduated from public high school in Massachusetts within four years of begin-
ning ninth grade (= 1 if they were reported as graduating; 0 de lo contrario).4 To test whether
dropout occurs early in high school I include an indicator of whether a student is still
enrolled in high school in grade 11 (ENROLL11) as an intermediate outcome. In addi-
ción, I deﬁne an indicator of whether a student passed both required exams (PASS), como
well as the continuous, standardized measures of performance on the math and ELA
exams.5 My ﬁnal outcome of interest is an indicator of whether a student earned an
industry-recognized certiﬁcate (IRC) while in high school. IRCs include Microsoft Of-
ﬁce, Cisco Systems, and ServSafe certiﬁcations that signal speciﬁc skills and credentials
potentially valuable to employers in speciﬁc industries.

In my OLS approach, my key treatment variable is a dichotomous indicator of
whether a student enrolled in an RVTS during their ninth-grade year (RVTS9).6 yo discuto
that students in both treatment and control conditions should be equivalent in expec-
tation of future outcomes, conditional on observing the criteria for CTE eligibility in
eighth grade (Altonji, Elder, and Taber 2005).

All applicants to RVTSs are evaluated on three elements of their middle school
experiencia: transcripts, attendance, and discipline record. To improve the internal va-
lidity of my OLS estimates, I use prior measures of (1) eighth-grade attendance (a-
tal days present, DAYS), (2) academic performance (as measured by eighth-grade
Massachusetts Comprehensive Assessment System or MCAS scores in mathematics,
MCAS_M8), y (3) disciplinary record (total instances of in- or out-of-school suspen-
sión, IN_SUSP and OUT_SUSP, respectivamente) as proxies for these known application
criteria. The attendance and discipline records are identical to those used in evaluating
eligibility for RVTSs, and the test scores are a proxy for prior academic performance. I

4. Acerca de 3 percent of the sample transfer out of state before I observe whether they graduate from high school.
I propose to test the sensitivity of my results by deﬁning these students as graduates or nongraduates. I also
examined ﬁve-year graduation probabilities and ﬁnd no diﬀerence in the eﬀects.

5. By using both the passing threshold required to earn a diploma and continuous scores, I gain greater perspective

on how earning the diploma relates to levels of human capital.
I choose this deﬁnition to minimize selection bias. Conditional on having no prior formal exposure to CTE,
students who experience CTE in grade 9 or not may choose to exit or enter CTE in a subsequent year. By deﬁning
exposure as a binary measure of exposure in grade 9 I seek to minimize bias related to post-grade 9 selección
into or out of CTE.

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127

Effect of Career and Technical Education

include indicators of gender, carrera, disability status, and English-language learner status
to improve the precision of my estimates, and a dichotomous indicator for whether a
student is eligible to receive free or reduced-price lunch (FRPL).7

In my RD approach, I deﬁne the forcing variable as a student’s score on her appli-
cation for admission (SCORE), and also generate a dichotomous indicator, OFFER, a
describe whether a student was oﬀered a seat in an oversubscribed RVTS. The variable
ENROLL is a dichotomous indicator describing whether a student accepted the oﬀer to
attend a CTE program after participating in the admissions process.

Análisis de los datos
I ﬁrst produce estimates using OLS by specifying the following model:

Yigrc = α0 + α1RVTS9igrc + α2FRPLigrc + α3(FRPL × RVTS9igrc )

(cid:2)
+ X
i

γ + πg + τr + ωc + εigrc,

(1)

where Yigrc is the generic outcome Y for student i in cohort g from town r, in occu-
pational cluster c, and πg, τr, ωc represent ﬁxed eﬀects for cohort, town of residence,
and occupational cluster, respectively.8 The parameters of focal research interest are
α1, which represents the population relationship between CTE treatment on the prob-
ability of achieving the outcome for a student who is not low-income, and the sum
of parameters α1 and α3, which represents the analogous relationship for a student
whose family is lower income.9 All of my estimates use heteroskedasticity-robust stan-
dard errors clustered at the high school level to account for autocorrelation of errors for
students in the same school.

In my regression-discontinuity approach, I estimate the causal eﬀects of participat-
ing in CTE by capitalizing on student enrollment in RVTSs that are oversubscribed.
During the admissions process, student applicants to oversubscribed RVTSs receive
an admission ranking based on a composite score made up of multiple application cri-
teria, and are admitted one-by-one, highest to lowest, until all seats are ﬁlled. Porque
the last students who are admitted diﬀer very little in their overall admissions score
from students who just miss being oﬀered a spot in an RVTS, I posit that the similarity
among students at the margins of admission make them arguably equal in expectation
at the admit/nonadmit discontinuity on the admissions-score forcing variable (Imbens
and Lemieux 2008; Murnane and Willett 2011).

I implement a standard fuzzy RD design (Imbens and Lemieux 2008; Murnane
and Willett 2011) in conjunction with a triangular kernel, using two-stage least squares
within a local-linear regression framework. In the ﬁrst stage, I model the probability
that a student receiving an oﬀer of admission takes up the oﬀer and enrolls. In the sec-
ond stage, I capitalize on the exogenous variation in enrollment, carved out by my in-
strument (Angrist, Imbens, and Rubin 1996), to estimate the causal eﬀect of enrollment

7. Actual indicators of whether a student applied and was denied are not available in the administrative data.
8. My preferred speciﬁcation does not include the ﬁxed eﬀects for occupational cluster as it is not possible to
match on this criterion since no one in the counterfactual setting is associated with an occupational area. Mi
results are not sensitive to the exclusion of these ﬁxed eﬀects.
In my results, I present the combined coeﬃcients α1 and α3 to show the eﬀects for lower-income students.
Coeﬃcients were combined using the lincom command in Stata (StataCorp, College Station, Texas).

128

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shaun m. Dougherty

sobre los resultados de los estudiantes. I specify my general ﬁrst-stage linear probability model for stu-
dent i in cohort c in school s, como sigue:

PAG(ENROLL = 1)circuitos integrados

= α0 + α1OFFERics + α2CSCOREics + α3CSCORE × OFFERics

(cid:2)
+ X
i

i + ϕc + γs + δics,

(2)

where φ and γ represent the ﬁxed eﬀects of cohort and school, and δ is a residual. En
this model, I recenter the student’s admissions score at the unique admissions cutoﬀ
used in her particular school and year (CSCORE). Standard errors are clustered on the
discrete values of the forcing variable (CSCORE) (Lee and Card 2008).

My second-stage model takes the form:

Yics = π0 + π1

(cid:2)ENROLLics + π2CSCOREics + π3CSCORE × OFFERics + X

(cid:2)
i

(cid:12)

+ ϕc + γs + εics,

(3)

where Yics represents the generic outcome. The parameter of interest is π1, representing
the population causal eﬀect of participating in an oversubscribed CTE school on later
outcomes among students at the margins of being admitted. I estimate these models
using a triangular kernel and preference the optimal bandwidth suggested by Imbens
and Kalyanaraman (2012) when interpreting results.10 To test for the heterogeneity of
eﬀects by lower-income status I also interact free- or reduced-price lunch eligibility with
the oﬀer indicator and add it to both the ﬁrst and second stages, while allowing the rela-
tionship between the forcing variable and outcomes to also be ﬂexible by income status.

4 . RESULTADOS
OLS Estimates
In panel A of table 2, I present my OLS estimates of the impact of RVTSs’ participation
on student outcomes for higher-income students as well as their free or reduced-price
lunch–eligible peers.11 In all cases the appropriate reference group includes students
who did not attend an RVTS in grade 9, including nonparticipants and those in a com-
prehensive CTE setting. In the ﬁrst row are estimates of the aggregate eﬀects of RVTS
participation for higher-income students, and in row 2 are the estimates for students
who are free or reduced-price lunch–eligible. In panel B, I report analogous results
using only students in the RD sample (discussed below).

My OLS estimates suggest that CTE participation in an RVTS is associated with
higher probabilities of graduating from high school on time, remaining enrolled in
high school through grade 11, earning an industry-recognized certiﬁcate, and passing
both exams required to earn a diploma.12 Eﬀects on graduation, persisting in high
escuela, and passing both exams required for graduation are larger for low-income
students and statistically diﬀerent from those of their higher-income peers. There is

10. See also Calonico, cattáneo, and Titiunik (2014) for a discussion of optimal bandwidth choice.
11.

In table A.1, I provide evidence that OLS results are similar to matching estimates using a variety of matching
estimators.

12. My results are not sensitive to my use of a measure of graduation in ﬁve years (results are available from the

author upon request).

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129

Effect of Career and Technical Education

Mesa 2. OLS Estimates of the Effect of Attending a Regional Vocational and Technical School

Graduated
(1)

Enrolled
Calificación 11
(2)

Earned
Certificate
(3)

Matemáticas
Score
(4)

ELLA
puntaje
(5)

Pass
Ambos
(6)

Grupo A: Overall Sample

Higher income

Lower income

0.114***
(0.008)
0.21***
(0.016)

0.086***
(0.006)
0.17***
(0.011)

0.312***
(0.050)
0.30***
(0.051)

−0,002
(0.013)
0.09***
(0.020)

−0.051*
(0.027)
0.08***
(0.035)

0.114***
(0.008)
0.19***
(0.013)

norte

417,215

375,961

378,358

417,215

Grupo B: Regression Discontinuity Sample

Higher income

Lower income

0.145***
(0.014)
0.23***
(0.020)

0.059***
(0.010)
0.17***
(0.015)

0.174***
(0.010)
0.21***
(0.013)

0.140***
(0.025)
0.20***
(0.029)

norte

4,885

4,422

0.102***
(0.030)
0.28***
(0.040)

4,475

0.013
(0.015)
0.07***
(0.017)

4,885

Notas: Heteroskedasticity robust standard errors clustered by school are in parentheses. Estimates are of
the effects of attending an RVTS in grade 9 relative to participating in any program (CTE or not) in a com-
prehensive high school. The coefficients shown are generated using ordinary least squares. All specifications
include fixed effects for graduation cohort and grade 8 town-of-residence. All estimates control for observable
student characteristics including race, género, income, disability, and English language-learner status (también
as observable proxies for characteristics used to admit students to RVTSs); middle school test scores, sus-
pensions, and attendance rate. CTE: career and technical education; RVTS: regional vocational and technical
high school; ELLA: English language arts.
*pag < 0.10; ***p < 0.01. no clear eﬀect on student test scores among higher-income students, but suggestive statistical evidence exists of a positive impact on lower-income students who remain in school long enough to be tested. I cannot make strong inferences on test-score out- comes because the sample of test students is smaller than the general sample. Using common bounding techniques to account for selection out of the sample, I cannot rule out the possibility of a negative impact on higher-income students and a null eﬀect on lower-income students.13 Regression Discontinuity Estimates To establish the internal validity of my RD estimates, I demonstrate that students im- mediately on either side of the discontinuity for admissions are similar on observable characteristics, and verify that the forcing variable is smooth and continuous at the cut- oﬀ, to satisfy the assumption that an applicant’s position cannot be manipulated relative to the oﬀer threshold. In table 3 I present evidence to suggest that my treatment and control groups are equal in expectation on a selection of observable characteristics. I ﬁt equation 1, replacing the outcome with each covariate, and ﬁnd only one diﬀerence of note—that there appears to be fewer low-income students admitted than denied ad- mission.14 To establish the continuity of the forcing variable, I display a histogram of 13. Selection analyses were undertaken using Stata routines to apply a Heckman correction or Lee bounds. 14. Graphical analysis suggests this could be driven by assumptions of linearity. As I show below, including controls to account for this one potential imbalance does not aﬀect the statistical or substantive conclusions of the results. Results are also not sensitive to removing the one school that contributes to this imbalance, though it is retained in the analysis for the added statistical power. 130 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d f . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Shaun M. Dougherty Table 3. Estimates of Differences in Observable Characteristics Between Eligible and Noneligible Regional Technical School Applicants Male (1) 0.053 (0.046) 3,037 0.082 (0.079) 1,023 0.052 (0.050) 2,606 0.573 Black (2) −0.024 (0.016) 4,229 −0.013 (0.019) 1,023 −0.023 (0.019) 2,606 0.058 Latino (3) 0.015 (0.015) 2,291 −0.027 (0.031) 1,023 0.016 (0.014) 2,606 0.150 Asian (4) −0.001 (0.004) 2,291 0.001 (0.004) 1,023 −0.003 (0.004) 2,606 0.005 White (5) 0.020 (0.036) 2,108 0.041 (0.053) 1,023 0.026 (0.030) 2,606 0.806 ELL (6) 0.007 (0.009) 2,451 −0.003 (0.008) 1,023 0.007 (0.008) 2,606 0.015 IK bandwidth N Bandwidth = 6 N Bandwidth = 15 N µ Disability Status (7) −0.082 (0.049) 2,108 −0.134** (0.047) 1,023 −0.062 (0.047) 2,606 0.214 Low Income (8) Grade 8 Math Score (9) −0.084*** (0.016) 2,291 −0.107*** (0.019) 1,023 −0.070*** (0.018) 2,606 0.408 0.108 (0.070) 2,689 0.100 (0.069) 1,001 0.108 (0.071) 2,547 −0.209 Notes: Heteroskedasticity robust standard errors clustered by application score are in parentheses. Each coefficient is the reduced form estimate of the relationship between offer of admission and the listed covariate. The coefficients shown are generated by local linear regression using a triangular kernel and specified bandwidth, and include cohort and school fixed effects. Also listed is the mean of the covariate for students just below the threshold for receiving an offer of admission. The sample includes the 2007–09 cohorts for which graduation outcomes are available. ELL: English language learner; IK: Imbens and Kalyanaraman 2012. **p < 0.05; ***p < 0.01. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d / . f Figure 1. Distribution of Application Scores. students by application score value on the recentered forcing variable (ﬁgure 1). Neither in the combined distribution (panel A), nor in the distributions of the forcing variable within individual schools (panels B, C, and D) do I observe evidence of manipulation. The process used to generate the application scores also supports the internal va- lidity of the research design. First, students received points (according to a ﬁxed set of rules) based on their middle school academic performance, attendance, and disci- plinary records. In addition, the fourth criteria—middle school counselor rating—was f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 131 Effect of Career and Technical Education l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d / f . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Figure 2. First-stage Probability of Enrolling as a Function of Receiving an Offer. submitted by the middle school and without knowledge of the cutoﬀ that was ultimately used to admit students, and therefore could not be used to manipulate a student’s po- sition relative to the cutoﬀ. The most credible threat to internal validity stems from the admissions interview, where administrators interviewed applicants. Nonetheless, conversations with admin- istrators and publicly available state documents (MADESE 2010) suggest such threats are minimal. First, interviewers did not know what score was to be used as the admis- sions cutoﬀ, and so could not have reliably manipulated a student’s position relative to that cutoﬀ. Second, interviewers followed set protocols with predetermined questions and processes for awarding points. Thus, the interview score, and a student’s position relative to the ultimate admissions cutoﬀ, should not have been subject to manipulation by either the applicant or the school.15 First Stage Results The credibility of my instrumental-variables approach relies on a strong ﬁrst stage that indicates having received an oﬀer to attend an RVTS results in higher probabilities of enrollment in an RVTS for students near the admissions cutoﬀ. This discontinuity in actual enrollment is demonstrated in ﬁgure 2, which displays the probability of having enrolled in an RVTS in ninth grade—as a function of a student’s recentered application score—for all three schools combined as well as individually. I indicate the point at which students ﬁrst receive an oﬀer (CSCORE >= 0) by the vertical dashed line and
demonstrate the clear jump at the cutoﬀ in probability of attending.

15.

I explore this further in section 5.

132

shaun m. Dougherty

Mesa 4. First-Stage Estimates of the Effect of an Offer of Admission on Take-up

IK bandwidth

norte
Bandwidth = 6

norte
Bandwidth = 15

All Schools
(1)

0.314***
(0.059)

School 1
(2)

0.324***
(0.043)

School 2
(3)

0.314***
(0.085)

28.2

57.1

13.6

1,756
0.278***
(0.061)

463
0.359***
(0.040)

20.9

79.6

1,023
0.384***
(0.056)

463
0.522***
(0.065)

499
0.368**
(0.118)

9.7

156
0.313***
(0.096)

School 3
(4)

0.251***
(0.088)

8.1

1,029

0.161
(0.131)

1.5

404
0.241***
(0.084)

46.8

65.0

10.7

8.3

norte
Bandwidth = IK, controls

2,606
0.309***
(0.060)

1,102
0.298***
(0.059)

406
0.291***
(0.075)

1,098
0.245***
(0.088)

26.8

25.2

15.1

7.8

norte
Bandwidth = IK, low income

1,756
0.326***
(0.085)

463
0.310**
(0.134)

499
0.372***
(0.064)

1,029
0.352***
(0.072)

14.7

5.4

34.1

23.7

norte
Bandwidth = IK, high income

norte

739
0.294***
(0.068)

18.7

1,017

441
0.222***
(0.044)

25.4

582

1,276
0.429***
(0.070)

1,031
0.367***
(0.071)

37.2

27.0

1,761

1,420

Notas: Heteroskedasticity robust standard errors clustered by score are in parentheses. Primero-
stage estimates show the impact of receiving an offer of admission on actual enrollment
in an RVTS. The estimates are generated using local linear regression in conjunction with a
triangular kernel and the specified bandwidth and cohort-by-school fixed effects. An offer of
admission is determined by having an admission score just above the cutoff specified for
a given school and year for students in the 2007 a través de 2009 cohorts. The last two rows
show heterogeneity in the first stage by low-income status in the IK bandwidth (Imbens and
Kalyanaraman 2012). Below each coefficient is the F-statistic associated with the eligibility
instrument. IK: Imbens and Kalyanaraman 2012.
**pag < 0.05; ***p < 0.01. In table 4, I present regression-based estimates in the diﬀerence in probability of en- rolling in an RVTS in ninth grade between students who received, and did not receive, an oﬀer of admission at the cut score. The parameter estimate of interest represents the jump in the average probability of enrolling in an RVTS for students who are just eligi- ble to receive the oﬀer relative to those who just missed receiving an oﬀer. My estimates of the ﬁrst-stage discontinuity suggest a clear jump in the probability of attending an RVTS as a function of receiving the oﬀer of admission. Point estimates of this jump are relatively stable across choices of bandwidth, though they diﬀer somewhat by school. In the combined sample, my F-statistics always substantially exceed the threshold of ten suggested by Stock, Wright, and Yogo (2002). Causal Impact of an Offer of Admission on Student Outcomes In ﬁgure 3, I provide visual evidence of discontinuities in my four outcomes of inter- est at the admissions cutoﬀ. There is an apparent discontinuity in the probability of l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d / . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 133 Effect of Career and Technical Education l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d / . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Figure 3. Reduced-form Impact of Offer of Admission for All Schools. graduating on time for students near the cutoﬀ who received an oﬀer of admission. There are also similar discontinuities in remaining students enrolled by eleventh grade and in the probability of earning a certiﬁcate. Evidence is inconclusive for whether a student passes both graduation exit exams, and no real evidence of a diﬀerence in test scores. Visually, the diﬀerence in the probability of graduating from high school for students near the cutoﬀ is about 10 percentage points. In table 5 I present my reduced-form estimates of the eﬀect of attending an RVTS, including heterogeneity by whether a student is free- or reduced-price lunch–eligible. My estimates suggest a large and positive impact of being oﬀered a spot in an RVTS near the admissions threshold on high school graduation. Using the IK bandwidth (Im- bens and Kalyanaraman 2012), I interpret the statistically signiﬁcant point estimate of 0.13 in column 1 as a 7 percentage-point jump in the probability that a higher-income student who is oﬀered admission to an oversubscribed RVTS graduates on time rel- ative to his peers who just missed receiving this oﬀer. There are also 5 percentage- point increases in the probability of remaining enrolled through eleventh grade, and earning an industry-recognized certiﬁcate for marginal students oﬀered admission. For lower-income students the graduation beneﬁts are slightly smaller and less precise for these outcomes, though including covariates in the last row boosts magnitude and pre- cision. Magnitudes of outcomes ﬂuctuate somewhat by bandwidth choice but do not change the substantive conclusions of the eﬀects. Estimates for lower-income students are more sensitive to these choices, and such ﬂuctuation could be related to the imbal- ance at the cutoﬀ. 134 Shaun M. Dougherty Table 5. Reduced-Form Estimates of the Effect of an Offer of Admission on High School Graduation Probability Higher income, IK bandwidth Lower-income offer N Higher income, bandwidth = 6 Lower-income offer N Higher income, bandwidth = 15 Lower-income offer N Higher income, IK bandwidth, controls Lower-income offer N µ Graduated (1) 0.133*** (0.023) 0.04 (0.034) 1,756 0.166*** (0.018) 0.08** (0.045) 1,023 0.095*** (0.026) 0.01 (0.029) 2,606 0.074*** (0.024) 0.10*** (0.033) 1,756 0.664 Enrolled Grade 11 (2) 0.055*** (0.019) 0.01 (0.028) 2,291 0.064*** (0.016) 0.02 (0.038) 1,023 0.048** (0.018) 0.01 (0.025) 2,606 0.027 (0.028) 0.05* (0.027) 2,291 0.858 Earned Certificate (3) 0.056*** (0.012) 0.04*** (0.014) 2,606 0.060*** (0.014) 0.04*** (0.011) 1,023 0.057*** (0.012) 0.04*** (0.014) 2,606 0.045*** (0.012) 0.04*** (0.015) 2,606 0.028 Math Score (4) 0.128** (0.056) −0.02 (0.067) 2,473 0.179*** (0.053) 0.02 (0.060) 903 0.131** (0.056) −0.02 (0.068) 2,336 −0.022 (0.048) −0.02 (0.091) 2,473 −0.303 ELA Score (5) 0.122 (0.097) −0.05 (0.082) 2,501 0.254** (0.099) 0.03 (0.070) 913 0.126 (0.098) −0.05 (0.083) 2,364 −0.008 (0.084) −0.04 (0.052) 2,501 −0.207 Pass Both (6) −0.009 (0.046) −0.02 (0.051) 1,756 −0.033 (0.052) −0.03 (0.063) 1,023 −0.019 (0.040) −0.03 (0.043) 2,606 −0.033 (0.042) −0.00 (0.054) 1,756 0.154 Notes: Heteroskedasticity robust standard errors clustered by score are in parentheses. The estimates shown are intent-to-treat effects generated using ordinary least squares and include school-by-year fixed effects and a triangular kernel, with standard errors clustered at the admission score level. Estimates do not include covariates unless otherwise noted. ELA: English language arts; IK: Imbens and Kalyanaraman 2012. *p < 0.10; **p < 0.05; ***p < 0.01. Because my RD sample consists of only three schools that represent thirteen (of twenty-six) such oversubscribed RVTSs, I rely on the OLS results in panel B of table 2 as evidence that the eﬀects estimated for this subsample are somewhat comparable to their peer schools. Though the RD sample is one percent the size of the overall sample, the point estimates and statistical signiﬁcance for attainment and persistence are quite similar. In the RD sample there is some evidence of a possible positive impact on test scores, especially for lower-income students. Given my limited sample, I argue that these schools—and the associated results—have reasonable though limited external validity in the context of nonurban Massachusetts RVTSs. Instrumental Variables Results In table 6, I present my instrumental variables (IV) estimates of the eﬀect of the treatment-on-the-treated, or the eﬀect of being admitted and enrolling in an RVTS ver- sus not. These estimates are simply my reduced-form estimates by income status scaled by their respective ﬁrst stage. These results suggest clear, large, positive eﬀects on grad- uation and earning an IRC, with less precise estimates on persistence and no eﬀects on test scores for the marginal student induced into an RVTS. Across speciﬁcations the magnitudes diﬀer, but in all cases there appear to be positive and similar eﬀects for both higher- and lower-income students. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d / . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 135 Effect of Career and Technical Education Table 6. Instrumental Variables Estimates of the Effect of Attending an RVTS on Student Outcomes Graduated (1) 0.349*** (0.047) 0.21*** (0.049) 1,756 0.528*** (0.077) 0.38*** (0.095) 1,023 0.202*** (0.063) 0.08 (0.063) 2,606 0.233*** (0.057) 0.32*** (0.059) 1,756 Enrolled Grade 11 (2) Earned Certificate (3) Math Score (4) 0.047* (0.026) 0.05* (0.028) 3,833 0.079 (0.061) 0.06 (0.084) 1,023 0.082*** (0.028) 0.08*** (0.033) 2,606 0.019 (0.037) 0.09*** (0.034) 3,833 0.136*** (0.028) 0.11*** (0.033) 2,606 0.204*** (0.019) 0.18*** (0.033) 1,023 0.135*** (0.028) 0.11*** (0.033) 2,606 0.114*** (0.032) 0.13*** (0.034) 2,606 0.253 (0.157) 0.04 (0.170) 2,473 0.577*** (0.169) 0.31* (0.163) 903 0.263 (0.161) 0.05 (0.173) 2,336 −0.052 (0.100) −0.05 (0.179) 2,473 ELA Score (5) 0.225 (0.253) −0.02 (0.227) 2,501 0.801** (0.387) 0.42 (0.308) 913 0.235 (0.257) −0.01 (0.231) 2,364 −0.029 (0.173) −0.09 (0.113) 2,501 Pass Both (6) −0.035 (0.139) −0.05 (0.153) 1,756 −0.115 (0.189) −0.11 (0.207) 1,023 −0.054 (0.105) −0.07 (0.114) 2,606 −0.087 (0.131) −0.04 (0.164) 1,756 IK BW high income IK lower income N BW = 6 high income BW = 6 lower income N BW = 15 high income BW = 15 lower income N IK BW high, controls IK BW lower, controls N Notes: Heteroskedasticity robust standard errors clustered by application score are in parentheses. IV estimates show the impact of attending an oversubscribed RVTS on each of the outcomes stated in the column heading, where attending an RVTS is instrumented by an offer of admission. The coefficients shown are generated by local linear regression using a triangular kernel of the listed bandwidth, including cohort-by-school fixed effects. The sample consists of those members of the 2007 through 2009 cohorts who are present in the data in eighth grade. BW: bandwidth; ELA: English language arts; IK: Imbens and Kalyanaraman 2012. *p < 0.10; **p < 0.05; ***p < 0.01. 5 . D I S C U S S I O N The results from my analyses suggest three important points. First, both of my ana- lytic strategies suggest a clear beneﬁt of attending an RVTS in grade 9 as measured by indicators of attainment (graduation, passing required exams) and speciﬁc forms of human capital (certiﬁcate completion). My OLS results suggest these eﬀects exist for the average student, and the RD estimates suggest that similar eﬀects may hold for the marginal student admitted to an oversubscribed RVTS. Second, eﬀects on attainment are larger for lower-income students in the OLS, but not as clearly larger in the RD sample, suggesting that average eﬀects might be larger for lower-income students on average, rather than when they are the marginal student in a more selective school. Third, eﬀects appear to accrue through persistence in school and acquisition of spe- ciﬁc human capital (IRCs) rather than a measurable improvement in general math and reading skills. Below, I brieﬂy address concerns about threats to validity, situate the ef- fects on attainment in the relevant literature on high school interventions, and consider the mechanisms through which these eﬀects might accrue. Threats to Validity Both my OLS and RD analytic approaches are susceptible to concerns about internal validity. In both cases I have outlined why these concerns should be minimized by the 136 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d . / f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Shaun M. Dougherty fact that the two approaches oﬀer corroborating evidence of the eﬀects of participating in CTE, particularly as it relates to persistence, high school graduation, and earning an IRC. In OLS the main concern is omitted variables bias—speciﬁcally, that even con- ditioning on known proxies for admission to an RVTS, as well as observable student characteristics and town of residence, students in RVTSs may be self-selected on unob- served characteristics. Evidence from my OLS models on the RD sample should sub- stantially address these concerns because that sample consists entirely of students who choose to apply to an RVTS, which should be correlated with most of the unobservable characteristics that could undermine causal inference in this setting. Thus, although strong ignorability (Rosenbaum and Rubin 1984) cannot be guaranteed, it may be a more reasonable assumption under these circumstances. I argue that the OLS esti- mates from the RD sample, which are nearly identical to the larger OLS sample, are less prone to omitted variables bias, and their similarity to the general results provides support—though imperfect—for interpreting the larger OLS estimates as causal.16 In my RD approach two concerns arise: (1) the potential imbalance in the share of students who are free- or reduced-price lunch eligible at the margin of admission, and (2) the potential endogeneity of the interview score for the total admissions score. I deal with the ﬁrst concern by including covariates in one speciﬁcation and showing that it does not change the overall set of ﬁndings. Although this is not perfect, it at least establishes that accounting for this imbalance statistically does not undermine the core results. To address the second concern, I capitalize on the fact that one of the three over- subscribed schools retained both overall admissions scores and subscores.17 I then test the sensitivity of my core results by removing the potentially endogenous interview subscores and replacing them with the average interview score for that application year so that all students were pulled to the mean on this element (while maintaining the original cutoﬀ score to determine the oﬀer of admission). Though this introduces more fuzziness to the ﬁrst stage, there is still a discontinuity and statistically signiﬁ- cant reduced-form estimates of scoring just above the admissions threshold (see ﬁg- ure A.2 and table A.2). This suggests that even removing the potential beneﬁt of an above-average interview score does not undermine the positive eﬀect of being oﬀered admission to an RVTS on the other elements of the application materials. Plausibility of Effect Magnitudes Although there are relatively few high-quality evaluations of systematic high school in- terventions that show eﬀects, my reduced-form and OLS estimates of the eﬀects of at- tending an RVTS in Massachusetts are comparable to existing evidence on these other interventions. The aggregate sample average treatment eﬀect using my OLS approach in both samples produced an estimate of about 10 percentage points, whereas my RD estimate of the intent-to-treat eﬀect was closer to 7 percentage points. These estimates 16. My nonparametric and parametric matching estimators also yield similar evidence (see table A.1). 17. The state does not require that historical records of application scores be stored, nor whether records of individual subscores be maintained. Thus, this speciﬁcation check is only possible in this one case in my data. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d f . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 137 Effect of Career and Technical Education are roughly in line with Deming et al. (2014), who demonstrated that changes in school- choice options in Charlotte-Mecklenburg resulted in a 5.5 percentage-point boost in the probability that lottery winners graduated from high school. Similarly, MDRC’s study of Talent Development High schools (Kemple, Herlihy, and Smith 2005) found a boost in the probability of high school completion of 8 percentage points for students who were randomly admitted to the schools. The New York small schools program (Bloom and Unterman 2014) saw increased probabilities of graduation on the order of 9 percentage points over a baseline 59 percent probability of graduation. In addi- tion, Rodríguez-Planas (2012) ﬁnds a bump of 5 percentage points in the probability of graduating high school as a result of a comprehensive mentoring program in grades 9 through 12. My IV estimates of the eﬀect of the treatment-on-the-treated suggest a larger eﬀect than these other interventions (table 6), although these eﬀects are for the marginal stu- dent admitted (LATE), rather than the average student who experiences the treatment (ATE). Using optimal bandwidths at each stage of my IV approach I estimate the local average treatment eﬀect at between 17 and 35 percentage points. As I show in the last row of table 5, the mean share of students who graduate from high school for those who just miss an oﬀer of admission to an oversubscribed RVTS in my sample was 0.66. This suggests that the marginal student was at high risk for not completing high school and so is perhaps less alarming. This low probability of graduating for the marginal student not receiving an oﬀer might also explain why the LATE is not diﬀerent for lower- and higher-income students. Presumably students on this margin of admission are facing multiple impediments to their potential graduation from high school and so family in- come may not be a diﬀerentiating characteristic on the admissions margin, though it appears to be in the general population. Mechanisms Though my analytic approaches do not allow for strong causal identiﬁcation of the mechanisms through which attending an RVTS aﬀects student outcomes, my choice of outcomes, the policy context, and related extant literature present some insights into how the eﬀects I estimate might be realized. First, if the RVTSs simply represent a higher-quality educational environment relative to a student’s residentially assigned school, the eﬀects may accrue through that mechanism. Earlier literature that explored the impact of choice-based educational settings suggests that choice can produce posi- tive impacts, provided the outside option represents an improvement in quality over a student’s assigned school (Angrist, Pathak, and Walters 2011; Deming 2011; Dobbie and Fryer 2013; Deming et al. 2014). Therefore, if the RVTSs oﬀer a higher-quality environ- ment than a student’s assigned school we might expect to ﬁnd positive eﬀects, even if enrolling in and attending an RVTS also improves a student’s match to an academic or technical program of interest. Said another way, peer eﬀects and environment might positively augment the positive impact of an improved match (Holzer, Linn, and Mon- they 2013; Deming et al. 2014). My descriptive data (table 1) show lower-average middle and high school test scores for students who attend RVTSs relative to students in com- prehensive schools. As a result, it seems implausible that diﬀerences in quality—as solely deﬁned by peer academic performance—would drive the attainment eﬀects I 138 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d f / . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Shaun M. Dougherty ﬁnd. Rather, other mechanisms may be more likely and oﬀer more speciﬁc pathways for these eﬀects. Below, I consider whether other elements of quality, speciﬁc to the RVTS treatment, might generate eﬀects. Second, it appears the overall story is more about impact on persistence and com- pletion than on inﬂuencing math and ELA learning (as measured by test scores). Evi- dence that the overall eﬀects are driven by persistence and completion is supported by the clear positive impact on high school graduation, as well as the evidence of better persistence through eleventh grade. These eﬀects are clear in both analytic approaches, though eﬀects on persistence for higher-income students in the RD analysis is less ap- parent. The absence of an eﬀect on test scores further suggests that the main beneﬁt of attending an RVTS is accruing to students through their higher probability of com- pleting high school, rather than higher general human capital (Becker 2009; Lazear 2009). Much higher rates of successful completion of IRCs also points to beneﬁts ac- cruing via accumulation of speciﬁc human capital (Becker 1962, 2009), although there are no reliable measures in the administrative data of other soft or noncognitive skills that may also accrue. Eﬀects appear to operate through persistence and earning of IRCs, which may sug- gest that students (or schools) understand the importance of the signaling (Spence 1973; Clark and Martorell 2014) value associated with completing a high school diploma or its equivalent (Murnane, Willett, and Tyler 2000; Tyler, Murnane, and Willett 2000). It may be that RVTS participation facilitates the development of speciﬁc human capital— as measured by IRCs—which may also inﬂuence persistence based on perceived labor market beneﬁts. Finally, the structure of the RVTS’s learning environment may make learning more relevant and engaging, while simultaneously reducing the stigma associated with par- ticipating in CTE, and providing better mentorship opportunities, even if the general education in math and English is comparable to another school setting. In addition to oﬀering clear connections between formal education and applied learning, RVTSs pro- vide substantial exposure to the same instructors across multiple years—providing the potential for informal mentoring that has been shown in other settings to improve stu- dents’ attachment to school (Black et al. 2010; DuBois et al. 2011). This is also consistent with work that has shown that CTE participation can positively impact students’ attach- ment to school (Plank, DeLuca, and Estacion 2008). In addition, RVTSs also oﬀer the potential for reduced stigma associated with participating in these programs relative to a comprehensive school setting. Although my empirical evidence cannot wholly sup- port this claim, prior work does suggest that students have historically been negatively selected into CTE (Donahoe and Tienda 1999). Such negative selection could increase the opportunity for stigma if CTE participation were synonymous with lower academic performance or misbehavior. Because all students in an RVTS participate in a CTE program, the risk for stigma associated with CTE in general is not possible, though between-program stigmatization could still occur. 6 . C O N C L U S I O N S Using rich administrative data from Massachusetts, I provide plausibly causal esti- mates of the beneﬁts to high school persistence and graduation, and the earning of l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d . / f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 139 Effect of Career and Technical Education IRCs, for students who participate in a unique model of CTE (where all students en- gage in some form of CTE). My estimates are among the ﬁrst to capitalize on knowledge of how students opt into a speciﬁc form of CTE delivery in high school as a means to understand the impact of CTE participation on human capital accumulation in high school. Although more is known about intensive models of CTE delivery internationally (Iannelli and Raﬀe 2007; Malamud and Pop-Eleches 2010; Busemeyer, Cattaneo, and Wolter 2011; Hanushek, Woessmann, and Zhang 2011; Van de Werfhorst 2011), as U.S.- based policy makers consider ways to oﬀer a breadth of educational pathways for their students, the Massachusetts model of RVTSs likely presents a novel and potentially ef- fective delivery mechanism for CTE speciﬁcally, and high school curricula in general. Importantly, these eﬀects are derived in a policy environment that requires evidence of basic competencies for all graduates, suggesting the beneﬁts of earning a diploma through an RVTS in Massachusetts do not require the sacriﬁce of accumulating a min- imally acceptable level of general human capital. The descriptive evidence I provide surrounding potential diﬀerences in access to these programs as a function of student’s eligibility for free or reduced-price lunch is also novel in that it focuses on the students who may most beneﬁt from skills and certiﬁcations that carry value on the labor market. Furthermore, because students from lower-income families are more likely to drop out of high school, demonstrating the beneﬁts of CTE participation on this outcome is particularly compelling from both an educational and social policy perspective. Despite working with a rich dataset and several identiﬁcation strategies, my anal- yses remain limited in their respective internal and external validity. Neverthless, the robustness of my ﬁndings to multiple identiﬁcation strategies bolsters my claim that the relationships I observe are real. Given the renewed policy focus on CTE, as well as preparing students to be college and career ready, states and districts should con- sider how the Massachusetts regional vocational and technical school models may be adapted to their own educational settings. Finally, there is ongoing work suggesting there are clear labor-market returns to some forms of certiﬁcates that can be earned in community college settings (Kriesman et al. 2013; Huﬀ Stevens, Kurlaender, and Grosz 2015; Xu and Trimble 2016). These papers suggest, unsurprisingly, that returns are higher in some areas (health services) than in others. Policy makers and researchers should continue to explore the potential for alignment in CTE-related oﬀerings across the secondary–postsecondary threshold. ACKNOWLEDGMENTS I am grateful to the Institute for Research on Poverty at the University of Wisconsin for funding this research (grant no. 456K470), and to the Smith Richardson Foundation for underwriting the July 2014 Building Human Capital and Economic Potential conference. I am also grateful to the Taubman Center for State and Local Policy at the Harvard Kennedy School and Mathematica Policy Research for material support in the early stages of this work. In addition, I am indebted to the thoughtful feedback and comments of Richard Murnane, John Willett, David Deming, Joshua Goodman, Carolyn Heinrich, Timothy Smeeding, Chris King, Peter Bergman, Stephen L. Ross, Eric Brunner, Kenneth Couch, Delia Furtado, Seth Gershensen, Kevin Hollenbeck, Benjamin Dalton, Stephen Lipscomb, Marni Bromberg, Danielle Pietro, Rebecca Unterman, and my fellow 140 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d . f / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Shaun M. Dougherty Early Career Scholars at the Institute for Research on Poverty, particularly Dan Kreisman. I’m grateful for the additional support of the Applied Microeconomics Seminar at the University of Connecticut. I also wish to acknowledge the time and commitment of Carrie Conaway and Paula Willis at the Massachusetts Department of Elementary and Secondary Education, as well as the multitude of school staﬀ who provided data and insight into the ﬁndings from this project. 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Dougherty Table A.1. Estimates Using Multiple Matching Estimators CEM (1) Propensity Score (2) 0.04*** (0.003) 410,176 0.053*** (0.003) 417,215 Inverse Propensity Weights (3) Nearest Neighbor Mahalanobis (4) 0.037*** (0.005) 417,215 0.049*** (0.003) 417,215 On-time graduation N Notes: Heteroskedasticity robust standard errors are in parentheses. Estimates of the sample average treatment effect of experiencing an RVTS in grade 9 on the probability of graduating on time from high school using multiple matching estimators. The sample consists of those members of the 2008 through 2015 cohorts who are present in the data in eighth grade. CEM: coarsened exact matching (see Iacus, King, and Porro 2012). ***p < 0.01. Table A.2. Reduced-form Estimates of the Effect of Attending an RVTS on Student Outcomes When Removing Potentially Endogenous Interview Score from Admissions Score Graduated (1) Earned Certificate (2) Math Score (3) ELA Score (4) Pass Both (5) IK bandwidth N Bandwidth = 6 N Bandwidth = 9 N Bandwidth = 12 N Bandwidth = 9, controls N 0.051*** (0.013) 560 0.051*** (0.013) 560 0.036** (0.016) 759 0.012 (0.02) 1,029 0.034** (0.015) 758 −0.058 (0.035) 715 −0.065 (0.036) 560 −0.051 (0.035) 759 −0.052 (0.035) 1,029 −0.056 (0.037) 758 0.152** (0.067) 661 0.212*** (0.049) 560 0.048 (0.09) 759 −0.014 (0.092) 1,029 0.012 (0.062) 758 0.118 (0.072) 661 0.154** (0.064) 560 −0.005 (0.099) 759 −0.069 (0.104) 1,029 0.011 (0.06) 758 −0.022 (0.06) 759 0.007 (0.058) 560 −0.022 (0.059) 759 −0.034 (0.053) 1,029 −0.017 (0.055) 758 Notes: Heteroskedasticity robust standard errors clustered by application score are in parentheses. Reduced- form estimates show the impact of attending an oversubscribed RVTS on student outcomes. In these models only one school is used. The forcing variable is the admissions scores purged of the interview component, and with the mean interview score imputed so that the initial cutoff score for admission could be retained to define eligibility for admission. This increases the fuzziness of the discontinuity, but arguably removes the only potentially endogenous element of application scores. The coefficients shown are generated by local linear regression using a triangular kernel of the listed bandwidth, including cohort fixed effects. The sample consists of those members of the 2007 through 2009 cohorts who are present in the data in eighth grade. ELA: English language arts; IK: Imbens and Kalyanaraman 2012. **p < 0.05; ***p < 0.01. Table A.3. Testing Functional Form Assumptions Graduated (1) 0.087*** (0.023) 1,756 Enrolled Grade 10 (2) 0.021 (0.013) 3,833 Earned Certificate (3) 0.045*** (0.011) Math Score (4) ELA Score (5) Pass Both (6) −0.019 (0.041) −0.022 (0.052) −0.020 (0.044) 2,606 2,473 2,501 1,756 Linear, BW = IK N l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d . / f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 147 Effect of Career and Technical Education Table A.3. Continued. Graduated (1) 0.141*** (0.041) 1,756 0.117*** (0.026) 1,023 0.120*** (0.033) 1,023 0.076** (0.022) 2,108 0.128*** (0.030) 2,108 0.057** (0.023) 2,606 0.127*** (0.029) 2,606 Enrolled Grade 10 (2) 0.040** (0.017) 3,833 0.017 (0.022) 1,023 −0.005 (0.043) 1,023 0.028 (0.017) 2,108 0.018 (0.024) 2,108 0.030** (0.014) 2,606 0.020 (0.022) 2,606 Earned Certificate (3) 0.048*** (0.013) 2,606 0.050*** (0.008) 1,023 0.027 (0.016) 1,023 0.046*** (0.011) 2,108 0.048*** (0.013) 2,108 0.045*** (0.011) 2,606 0.047*** (0.014) 2,606 Math Score (4) −0.027 (0.040) 2,473 −0.080 (0.074) 903 −0.075 (0.089) 903 −0.021 (0.040) 1,885 −0.046 (0.051) 1,885 −0.018 (0.042) 2,336 −0.030 (0.040) 2,336 ELA Score (5) 0.060 (0.076) 2,501 −0.006 (0.045) 913 0.024 (0.076) 913 −0.002 (0.053) 1,906 0.084 (0.073) 1,906 −0.020 (0.052) 2,364 0.061 (0.076) 2,364 Pass Both (6) −0.054 (0.077) 1,756 −0.038 (0.051) 1,023 −0.083 (0.091) 1,023 −0.021 (0.043) 2,108 −0.037 (0.071) 2,108 −0.027 (0.038) 2,606 −0.023 (0.063) 2,606 Up to quadratic, BW = IK N Linear, BW = 6 N Up to quadratic, BW = 6 N Linear, BW = 12 N Up to quadratic, BW = 12 N Linear, BW = 15 N Up to quadratic, BW = 15 N Notes: Heteroskedasticity robust standard errors clustered by score are in parentheses. The reduced form estimates reported here were generated using ordinary least squares with an indicator for whether a student received an offer of admission from an oversubscribed regional vocational and technical school. Estimates are reported across multiple bandwidths with both quadratic and linear specifications of the forcing variable included at each bandwidth. All models include individual-level covariates to improve precision, as well as fixed effects for graduation cohort and school. BW: bandwidth; ELA: English language arts; IK: Imbens and Kalyanaraman 2012. **p < 0.05; ***p < 0.01. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / 1 3 2 1 1 9 1 6 9 2 3 8 1 e d p _ a _ 0 0 2 2 4 p d f . / f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 148 shaun m. Dougherty image

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