The Influence of Dual Enrollment on Academic Performance and College Readiness: Differences by Socioeconomic Status
Authors
- First Online:
- Received:
DOI: 10.1007/s11162-012-9278-z
- Cite this article as:
- An, B.P. Res High Educ (2013) 54: 407. doi:10.1007/s11162-012-9278-z
- 4 Citations
- 1.8k Views
Abstract
I examine the influence of dual enrollment, a program that allows students to take college courses and earn college credits while in high school, on academic performance and college readiness. Advocates consider dual enrollment as a way to transition high school students into college, and they further claim that these programs benefit students from low socioeconomic status (SES). However, few researchers examine the impact of dual enrollment on academic performance and college readiness, in particular, whether SES differences exist in the impact of dual enrollment. Even fewer researchers consider the extent to which improved access to dual enrollment reduces SES gaps in academic performance and college readiness. I find that participation in dual enrollment increases first-year GPA and decreases the likelihood for remediation. I conduct sensitivity analysis and find that results are resilient to large unobserved confounders that could affect both selection to dual enrollment and the outcome. Moreover, I find that low-SES students benefit from dual enrollment as much as high-SES students. Finally, I find that differences in program participation account for little of the SES gap in GPA and remediation.
Keywords
Dual enrollmentConcurrent enrollmentAccelerated programsSES gapsIntroduction
How do we improve an individual’s persistence once they enter college? How do we mitigate social-group differences and create equal opportunities for all individuals? These questions motivate social scientists, educators, and policy makers interested in higher education. For example, one of the conditions for Race to the Top Funds is for states to implement reforms that improve student preparation for college success (U.S. Department of Education 2009). One strategy to improve academic performance and college readiness is to provide students with a college experience prior to postsecondary entry (Iatarola et al. 2011). For example, dual enrollment is an accelerated program that allows students to take college courses while in high school (Allen 2010; Blackboard Institute 2010). Dual enrollment is an inexpensive way for students to earn college credit—and participation is free in some states (Hoffman et al. 2008). Because dual enrollees are exposed to college materials, some policy makers and social scientists consider dual enrollment as a way to prepare better students for the rigors of college coursework. Dual enrollment proponents further advocate that increasing program participation would reduce socioeconomic status (SES) gaps in academic performance (Dual enrollment in Texas 2010; Hoffman et al. 2008; Lerner and Brand 2006).
- 1.
Does participation in dual enrollment improves students’ academic performance and college readiness?
- 2.
Are there SES differences in the influence of dual enrollment on academic performance and college readiness?
- 3.
Would equal participation in dual enrollment reduce SES gaps in academic performance and college readiness?
I begin with a discussion of the ways in which students are allocated to high school programs and use research in educational stratification to guide my discussion. I further use this allocation model in my analysis. I then discuss the importance of pre-college academic preparation on academic performance and readiness in college. Finally, I discuss how dual enrollment serves as a mean to raise pre-college academic preparation. However, participation in dual enrollment differs across social groups. I highlight research that shows differential participation in dual enrollment programs by SES.
Unequal Participation of High School Programs by SES
“Fourth generation” researchers in educational stratification note that institutional and organizational arrangements alter an individual’s educational trajectory, even if two individuals attain the same level at a prior transition (Hout and DiPrete 2006; Treiman and Ganzeboom 2000). Building on Blau and Duncan’s (1967) pioneering work on status attainment, Kerckhoff (1995) argues that paths along the status attainment model—for example, between social origins and education—differ based on the organization of the school. For instance, track placement affects academic achievement by affecting the dispersion of achievement (i.e., educational inequality) and the overall level of achievement (i.e., educational productivity) (Gamoran 1992). Research shows that individuals placed in the academic track learn more than those in the nonacademic track, suggesting that curricular tracks widen achievement gaps (Gamoran and Mare 1989). The participation of high school students in different track and curricular locations has important consequences for their postsecondary opportunities. For example, high school students who participated in an academic track are better prepared to transition to college than those who participated in a general track (Breen and Jonsson 2000; Gamoran and Mare 1989).
These qualitative distinctions within a given educational transition are especially important in the United States because there is less variation in the types of certificates offered to secondary school graduates than other countries (e.g., England and Germany) (Kerckhoff 2001). Students tend to have flexibility in choosing their schooling experience. Of course, students are influenced by other actors (e.g., parents, friends, and teachers) or school policy (e.g., minimum requirements to participate), but students in the United States are also not set in rigid and overarching tracks (Goldthorpe 1996; Lucas 1999; Lucas and Good 2001). This flexibility in program assignment provides families with greater opportunities to shape their child’s schooling experiences (Bidwell and Quiroz 1991).
Educational attainment requires a series of decisions that affect both the continuation or termination of schooling and the curricular pathways in which students participate. Given the myriad of considerations that factors into schooling decisions, parents and other significant members provide assistance that helps students navigate through these decisions (Engberg and Allen 2011; Hauser et al. 1983). As high school attainment reaches saturation—and as a consequence, college-degree attainment becomes increasingly the norm for an adequate standard of living—high-SES parents make strenuous and calculated efforts to guide their children through school in order to secure academic credentials that are superior in both content and prestige (Haveman and Smeeding 2006; Lucas 2001). The relationship between parents and children is important in transmitting parental resources and information to their children (Coleman 1988). Studies show that parent–child discussions regarding college and other academic issues influence the likelihood that a student applies to and participates in a postsecondary school (An 2010; Kim and Schneider 2005).
Moreover, high-SES parents are more likely involved with and invest towards their children’s college decisions than low-SES parents (An 2010; Charles et al. 2007). Low-SES parents tend to relinquish educational responsibilities and instead focus on responsibilities that foster natural growth (e.g., provision of love, food, comfort, and safety) (Lareau and Weininger 2008). Low-SES parents may be enthusiastic and exhibit great determination in their child’s educational success, but they are more likely than high-SES parents to engage in a “generic” relationship with teachers and school officials and display signs of intimidation and confusion when interacting with these officials. As a result, low-SES parents tend to exert less influence on guiding their children through the college-choice process than middle- and high-SES parents. By contrast, middle-SES parents are more inclined to micro-manage their children’s application experience in order to yield the best results. In addition to their own experience of attending college, middle- and high-SES parents are better able to procure school resources and academic programs that improve their child’s college prospects (Lareau and Weininger 2008).
Part of the educational advantage of middle- and high-SES parents is that they tend to place their children into higher track locations than their low-SES counterparts (Breen and Goldthorpe 1997; Breen and Jonsson 2000; Lucas 2001; Useem 1992). Although stratification researchers have shown that academic tracks and course-taking patterns in high school influence educational achievement and attainment, they devote less time on the role of accelerated programs (e.g., Advanced Placement [AP] and dual enrollment) on educational achievement and attainment. Accelerated programs expedite a student’s college experience by bringing college or college-like courses to his or her high school. Dual enrollment advocates often consider dual enrollment courses more rigorous and prestigious for college-bound students than courses taken from a traditional program (Blackboard Institute 2010; Immerwahr and Farkas 2006). Dual enrollees are further able to earn college credit while in high school, giving participants momentum into the next transition. Participation in dual enrollment therefore holds greater currency for postsecondary transitions than traditional high school programs and dual enrollment programs may serve as an effective means for affluent families to secure their social position (Bailey et al. 2002; Dual enrollment in Texas 2010; Museus et al. 2007).
Pre-College Academic Preparation on Academic Performance and College Readiness
A major concern among educators and policy makers is whether college entrants are prepared academically to handle college coursework. Studies show that high school academic preparation is a key determinant for college entry and success (Adelman 1999; Astin and Oseguera 2012). A one-grade increase in high school grade point average (GPA) is associated with a 0.31–0.37 point increase in first-year college GPA (Allen et al. 2008; Wolniak and Engberg 2010). The coursework students take in high school is perhaps even more important than grades for college success. Adelman (1999) attributes 41 % of the influence of pre-college academic resources (e.g., curriculum, test scores, and class rank) on a bachelor’s degree attainment to high school curriculum.
There are several reasons why pre-college preparation is important for college success. Coursework is a sequential process for several core academic subjects (Stevenson et al. 1994). For students to take the highest-level course of a subject they typically need to take its prerequisites; and after they show aptitude of the material—usually in the form of grades—they proceed to the next course level. A student’s pre-college experience and preparation solidify certain opportunities while marginalizing other opportunities (Schneider et al. 1998). Students do not simply “restart” at each new level of education, but rather they carry over skills, aspirations, and perceptions they develop or reinforce prior to college. Studies show a positive relation between pre-college academic preparation, and college enrollment and degree attainment (Adelman 2006; Bound et al. 2010; Gamoran and Mare 1989). Even if students have not mastered entirely material learned from the course, they develop other important skills. For instance, individuals who take advanced courses tend to have higher expectations of academic success and tend to think more critically than students who took a general curriculum course (Berends 1995).
Despite its importance for college success, many students enter college underprepared. Almost half of high school graduates are highly qualified for admission at a 4-year institution (Berkner and Chavez 1997). A consequence to the high level of academic under-preparation is the degree to which college entrants require remediation. Twenty-eight percent of entering freshman enrolled in at least one remedial course in reading, writing, or math (Parsad and Lewis 2003). Moreover, over 40 % of students enrolled in at least one remedial course within 8 years after college entrance (NCES 2004). Several researchers attribute remedial course-taking patterns as a key indicator of college readiness (Baker et al. 2005; Conley 2007; Kim and Bragg 2008). Critics argue that remediation is costly and delays time to college-degree completion because individuals often do not earn credit that fulfills a degree requirement. In general, studies show that students who enroll in a remedial course are less successful in college than students who do not enroll in a remedial course (Attewell et al. 2006; Bettinger and Long 2004).
Some social scientists and policy makers attribute academic under-preparation to a misalignment between secondary and postsecondary systems (Venezia et al. 2007). Although academic standards are enforced in secondary education, these standards do not necessarily align with college requirements (Carnevale 2007). As a result, many students enter college underprepared for coursework despite meeting high school standards.
The Role of Dual Enrollment on Academic Preparation and College Readiness
Social scientists and policy makers consider dual enrollment as a way to align secondary and postsecondary systems (Allen 2010; Hoffman et al. 2008). Dual enrollment requires high school–college partnerships, which brings administrators from both education systems together. Students who participate in dual enrollment further take actual college courses, thereby meeting college standards (Allen 2010; Blackboard Institute 2010).
A main objective of dual enrollment is to increase the depth of study for subjects in high school. For some students, even high school honors courses do not provide the same level of intellectual stimulation as their equivalent dual enrollment course (Johnson and Brophy 2006; Olszewski-Kubilius 1998). Dual enrollment further reduces “senioritis,” which refers to students’ disengagement with a rigorous course regiment during their senior year of high school. Most college-bound students apply to college in the fall of their senior year of high school. Therefore, students have little incentive to work hard during their final semester of high school, which affects their academic performance in college since students take almost 6 months off from a rigorous course curriculum (Andrews 2004; Bailey et al. 2002). Some have charged senioritis as a contributor to the high level of remediation and low level of persistence once students enter college (Kirst 2001). Dual enrollment combats senioritis by providing high school students with a challenging coursework and incentives, through college credit accumulation, in order to maintain a high level of motivation and commitment.
An additional benefit of dual enrollment is that participants have the opportunity to replace their vague notions of college with a more realistic set of expectations. Dual enrollees are able to judge the extent they are able to handle college coursework. Those without proper preparation may attempt to “catch up” and prepare themselves for college or they may decide to seek alternative routes. Students further realize that, as college students, they are treated differently than they were as high school students. For example, college courses require students to place higher levels of self-induced accountability than in high school because there are fewer mechanisms (e.g., homework, weekly quizzes) that monitor the extent students are keeping up with the material (Bailey et al. 2002; Pierce 2001). Moreover, dual enrollees tend to view their high school teachers as “parental figures” where, by contrast, college instructors tend to focus more on specific learning areas (Huntley and Schuh 2002–2003).
Studies show that students who participated in dual enrollment are more successful academically in college than those who did not participate in these programs. Researchers find that participation in dual enrollment is positively related to college GPA, persistence, and degree attainment (Allen and Dadgar 2012; Karp et al. 2007; Swanson 2008). Moreover, students who participated in dual enrollment were less likely to take a remedial math course than nonparticipants (Kim and Bragg 2008).
Who Benefits from Dual Enrollment?
An obstacle to dual enrollment participation is that these programs generally have academic requirements for participation. For example, Florida requires students to have a 3.0 high school GPA, pass appropriate sections of the college placement test, and fulfill additional admission criteria in the articulation agreement between the postsecondary institution and the school district in order to participate in college academic courses (Hoffman et al. 2008). Therefore, high-achieving students are typically the ones to reap the potential benefits of dual enrollment.
Prior research has established the relation between social background and academic achievement. Studies show that differences in SES account for a large portion of the black–white achievement gap (Fryer and Levitt 2004). SES further exerts a direct association, about 0.27 standard deviations, on academic achievement (Sirin 2005). Not only does students’ class origin influence their academic achievement, but it also affects their academic choices within the education system, even among those with similar levels of achievement (Boudon 1974). Privileged students are more likely to take advanced courses than their less-privileged counterparts (Gamoran and Mare 1989; Lucas 2001; Lucas and Berends 2002). Mid- and high-SES parents, with perhaps more extensive knowledge of the importance of courses on their children’s education, tend to be more involved with their children’s academic progress than low-SES parents. If necessary, mid- and high-SES parents dismiss and overrule teachers’ recommendations to place their children in non-advanced courses (Lucas 2001; Useem 1992). Research shows that approximately 65 % of high school graduates with a parent who attained at least a bachelor’s degree are highly qualified for admission at a 4-year institution. By contrast, 45 % of high school graduates without a parent who attended college are highly qualified for admission at a 4-year institution (Berkner and Chavez 1997).
Perhaps not surprisingly, white and high-SES students are more likely to participate in dual enrollment than minority and low-SES students (Meade and Hofmann 2007; Prescott 2006). In New York City, black and Latino students represent 14 %–15 % of 11- and 12th-grade students, but they each represent 6 % of dual enrollment participants (Meade and Hofmann 2007). Dual enrollment, it seems is yet another way for high-achieving—and by association white and high-SES students—to improve their college preparation even though they are the least in need.
Given unequal participation rates of dual enrollment and its benefits on college success, several dual enrollment proponents have pushed forth an equity agenda where dual enrollment reaches a wider range of students. At least nine states have or are considering policies that allow all students the opportunity to acquire college credit while in high school (Hoffman 2007). Proponents are interested in the extent to which dual enrollment improves academic performance and college readiness for low-SES students (Bailey et al. 2002; Bragg et al. 2006; Hoffman et al. 2008). Some even contend that equal access to dual enrollment programs may mitigate SES gaps in academic performance and college readiness (Dual enrollment in Texas 2010; Hoffman et al. 2008; Lerner and Brand 2006).
Unequal access to dual enrollment across social divides becomes relevant if those who traditionally do not participate in dual enrollment benefit from participation. Proponents of “dual enrollment for all” contend that more students would benefit if they had the opportunity (Bailey et al. 2002; Dual enrollment in Texas 2010; Hoffman et al. 2008). Opponents, however, argue that allowing all students to participate in dual enrollment may dilute the quality of academic content or that low-achieving students will have difficulty keeping pace in these courses (Bailey et al. 2002). There is little research that examines whether a wider audience of students would benefit from dual enrollment participation. An exception is Karp et al.’s (2007) study where they find that low-SES students are more likely to benefit from dual enrollment participation than high-SES students. It is therefore important to examine the influence of dual enrollment on academic performance and college readiness, and whether these programs equally benefit students across the SES spectrum.
Data and Methods
I used data from the Beginning Postsecondary Students Longitudinal Study (BPS:04/09) and the 2009 Postsecondary Education Transcript Study (PETS:09) to assess the impact of dual enrollment on academic performance and college readiness. BPS:04/09 is a sample of first-time college students in 2004. Investigators surveyed students again in 2006 and 2009 (Wine et al. 2011). Because I am interested in academic performance and college readiness, my sample comprised of respondents who attended a postsecondary school and who had a postsecondary course transcript.
The initial sample contained 17,170 eligible respondents, undergraduate freshman or first-year students who had not completed prior postsecondary degrees and who had not completed a postsecondary class toward a postsecondary degree or award since completing high school. The sample was reduced to 14,370 and 15,630 (first-year GPA and remediation, respectively) due to unattained college transcripts and missing information from dependent variables. I further restricted my sample to those under age 24, because investigators asked respondents certain questions (e.g., SAT or ACT scores and dual enrollment participation) for only respondents under age 24. This restriction leaves an analytical sample of 13,230 for models that estimate effects on first-year GPA and a sample of 14,090 for models that estimate effects on remediation.
Dependent Variable
I measured academic performance as a student’s first-year GPA. Although not the only measure of academic performance, college GPA has important consequences for course-taking opportunities and advancement. First-year GPA came from college transcript records and investigators computed a student’s GPA for all college courses within the first 12 months of his or her college entry. Investigators scaled GPA as a four-point metric, where 0.0 represented an “F” letter grade and 4.0 represented an “A” letter grade. In supplementary analysis (not shown), I estimated cumulative GPA of a student’s college career and found that the relation between dual enrollment and GPA did not change based on how I measured GPA.
I measured college readiness as whether a student took at least one remedial course during college. Remediation as a measure of college readiness is consistent with prior research (Kim and Bragg 2008). This measure included courses in several subjects, such as English (and business English), pre-college math (e.g., arithmetic), basic skills, basic science (e.g., preparatory chemistry), and vocational skills (e.g., job skills) (Bryan and Simone 2012). With the PETS:09 study, the remediation variable could either take the form of a categorical outcome (e.g., took remediation or not) or a continuous outcome (e.g., number of remedial courses taken). I used a binary outcome of course remediation for two reasons. First, I found that about 56 % of BPS:04/09 respondents did not take a remedial course during college. Second, among respondents who took a remedial course, about 40 % of them required only one course.
Dual Enrollment
I used a binary indicator of dual enrollment participation (see “Appendix” for a description of variables). Nonparticipants in the control group comprised of those who participated in other high school and exam-based credit programs (e.g., traditional programs, and Advanced Placement programs and exams). Unfortunately, investigators did not collect the number of credits students accumulated through dual enrollment, and as a result, I was unable to examine “dosage” effects of dual enrollment. Although a binary treatment of dual enrollment limits inferences I can make about dual enrollment effects, an important policy question remains whether dual enrollment provides value-added benefits for students, especially given the paucity of rigorous studies on dual enrollment. Furthermore, the methodological development to accommodate multi-dose treatments of the propensity score matching model is in its early stages. In addition, the sensitivity analysis that I used required a binary treatment assignment.
Control Variables
I included several indicators that influence dual enrollment participation. I included measures of race, gender, family background, family structure, number of siblings in college, nativity, language spoken at home, and age. I coded race as black, Asian, Latino, other racial group, biracial, and white (omitted category). Family background comprised of parents’ education, family income, and home ownership.
College aspirations begin early in a student’s academic career. By ninth grade, many students have developed aspirations to attend college (Cabrera and La Nasa 2001). In turn, students who envision themselves attending college act in ways that prepares them for college participation (Morgan 2002). The number of colleges to which the student applied, whether the student consulted a published list of college rankings before selecting a college, and what the student considered important when choosing a college are measures of college expectations.
Prior studies show that dual enrollment participation often requires students to meet minimum academic requirements (Blackboard Institute 2010; Hoffman et al. 2008; Karp et al. 2004). Therefore, high-achieving students are more likely to participate in dual enrollment than low-achieving students. I included academic indicators such as students’ high school GPA, SAT scores, and their course history. For students who took the ACT exam, I converted their ACT score into an SAT score. Researchers note course-taking patterns in high school influence college success (Adelman 1999; Cabrera and La Nasa 2001; Lucas 2001). I included eligibility for the Academic Competitiveness Grants (ACG) and the highest level math course as measures of coursework rigor. Although not enacted until 2006, investigators created a measure of whether students were eligible for ACG had the program been in effect in 2004. To become eligible for ACG, students would need to complete at least 4 years of English, 3 years of social sciences, 3 years of math, 3 years of laboratory science, and 1 year of foreign language. Finally, I included whether a student attended a private high school.
I used multiple imputation to handle missing data, in which I created 20 replications of the data set. Once I imputed missing values of independent variables, however, I removed imputed values from the dependent variable. Imputed values of the dependent variable add little to estimates and may induce noise (von Hippel 2007).
Effects of dual enrollment on academic performance and college readiness
GPA 1st year | GPA | Remedial course | Remedial | |||||
---|---|---|---|---|---|---|---|---|
E.S. | FMI | MCE | θ | FMI | MCE | |||
Panel A | ||||||||
Naïve (S.E.) | 0.23*** (0.02) | 0.25 | −0.13*** (0.01) | 0.58 | ||||
Propensity score matching (S.E.) | 0.11*** (0.02) | 0.13 | 0.013 | 0.0005 | −0.06*** (0.01) | 0.78 | 0.033 | 0.0004 |
Parental education | GPA (1st year) | GPA | Remedial course | Remedial | ||||
---|---|---|---|---|---|---|---|---|
E.S. | FMI | MCE | E.S. | FMI | MCE | |||
Panel B | ||||||||
H.S. or less (S.E.) | 0.09* (0.05) | 0.09 | 0.008 | 0.0009 | −0.04^{†} (0.02) | 0.86 | 0.019 | 0.0007 |
Some college (S.E.) | 0.14*** (0.04) | 0.16 | 0.023 | 0.0013 | −0.04* (0.02) | 0.84 | 0.025 | 0.0007 |
Bachelor’s degree (S.E.) | 0.08* (0.04) | 0.10 | 0.008 | 0.0007 | −0.06** (0.02) | 0.75 | 0.014 | 0.0005 |
Post-bachelor’s (S.E.) | 0.08* (0.03) | 0.10 | 0.009 | 0.0007 | −0.06*** (0.02) | 0.71 | 0.005 | 0.0003 |
I employed a propensity score matching model to assess the impact of dual enrollment on academic performance and college readiness. However, this approach is vulnerable to hidden bias. I further conducted sensitivity analyses to examine the extent to which hidden bias affects my results.
Analytical Procedures
Estimating a Selection Equation
The propensity score matching model uses a single pretreatment balancing score—the propensity score—that represents the conditional probability of dual enrollment participation given covariates and potential outcomes. In this approach, I made a conditional independence assumption (CIA) where assignment to dual enrollment is unrelated to the potential outcome of nonparticipants after I adjusted on observed covariates (Ichino et al. 2008). To estimate dual enrollment effects, I matched dual enrollees with observationally equivalent non-dual enrollees based on their propensity score.^{1}
The propensity score matching model assumes that, once conditioning on covariates, assignment to treatment is ignorable. In other words, I assumed that after accounting for observed covariates, how students are selected to participate in dual enrollment is unrelated to unobserved indicators that affect the outcome. Although I included covariates related to program assignment and the college outcome, unknown confounders may continue to influence program selection and the outcome. To address the issue of hidden bias, I conducted sensitivity analysis.
Sensitivity Analysis
I manipulated p_{ij}, which altered U’s association to selection and outcome. I assessed how measured changes to U influenced the relation between dual enrollment, and academic performance and college readiness. This approach does not identify whether hidden bias exists, but instead quantifies the strength of association an unobserved confounder would need to be in order to undermine results. It remains up to the researcher to determine the plausibility of an unobserved indicator that could produce these selection and outcome effects.
Researchers have applied this approach to test the sensitivity of their results to measured unobserved confounders (Alvarado and Turley 2012; Doyle 2009; Harding 2003). The sensitivity analysis shows the point in which U terminates the estimated program effect on the outcome. Researchers still need to gauge the seriousness of a potential unobserved confounder in relation to the estimate from the propensity score matching model. One approach that researchers use to guide their decisions is to calibrate U to empirically and theoretically important covariates. For example, Alvarado and Turley (2012) investigate the relation between college-bound friends and where students apply to college. They find that having four or more college-bound friends increase the likelihood of applying to a 4-year college for both white and Latino students. Furthermore, their results are robust to unobserved confounders larger than any indicator they included in their model.
Results
Table 1 shows the impact of dual enrollment on academic performance and college readiness. I first report naïve estimates of dual enrollment (see “Naïve”), which is simply the mean difference between dual enrollees and non-dual enrollees. Naïve estimates show that individuals who participated in dual enrollment performed substantially better in college than nonparticipants. For example, dual enrollees earned a GPA that is 0.23 points higher than non-dual enrollees. Put differently, dual enrollees earned a GPA that was 0.25 standard deviations higher than non-dual enrollees (see “GPA E.S.”). Furthermore, students who participated in dual enrollment are less likely to take a remedial course than nonparticipants. In the naïve estimates, there is a 13 percentage-point difference in the likelihood of taking a remedial course between dual enrollees and non-dual enrollees.
Results from the naïve estimates show substantial benefits of dual enrollment on academic performance and college readiness. These estimates, however, may not only reflect the impact of dual enrollment, but they may also reflect baseline differences in students across programs. The second set of estimates (titled, “Propensity score matching”) reports the influence of dual enrollment after accounting for observed covariates that potentially confound results.
Compared to naïve estimates, results from the propensity score matching model show that over half of the dual enrollment advantage is due to observed student differences across programs. Even after adjusting for covariates, however, dual enrollment continues to influence academic performance and college readiness. For example, students who participated in dual enrollment earned a GPA that is 0.11 points higher than comparable students who did not participate in dual enrollment. Although about half of the estimated effect of dual enrollment on remediation is attributable to observed covariates, from −0.13 (naïve estimates) to −0.06 (propensity score matching model), a nontrivial difference remains. Dual enrollees are 6 percentage points lower in their probability to take a remedial course than non-dual enrollees.
Similar to previous research, results from the propensity score matching model show the positive influence of dual enrollment on academic performance and college readiness. However, this approach assumes that participation in dual enrollment is unrelated to covariates that influence academic performance and college readiness, once I account for observed confounders. In the next set of analysis, I assess the extent to which results from the propensity score matching model are sensitive to potential unobserved confounders.
Following Ichino et al. (2008), I perform a sensitivity analysis where I derive program estimates under different patterns of deviation from CIA or selection on observables. I specify four sensitivity parameters, the association of D and U, in order to specify fully the joint distributions of (D, Y_{1}, U|X) and (D, Y_{2}, U|X) (Ichino et al. 2008). I artificially create U, which I use as an additional indicator in the selection model. Manipulating p_{ij}, I assign measured associations of U to selection and outcome. Comparing the estimates between models with and without the simulated U, I am able to assess the extent to which the estimate is robust to targeted failures of CIA (for a further explanation of this approach, see Ichino et al. 2008).
Results of Sensitivity Analysis
Sensitivity analysis: effect of “killing” confounders on academic performance and college readiness
Outcome effect (row) (first-year GPA ) | Selection effect (column) (s = p_{1∙}–p_{2∙}) | |||||
---|---|---|---|---|---|---|
(r = p_{21}–p_{22}) | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 |
0.05 | 0.08 [1.44, 1.69] | 0.08 [1.40, 2.18] | 0.08 [1.35, 2.85] | 0.08 [1.31, 3.70] | 0.08 [1.28, 4.47] | 0.07 [1.32, 5.54] |
0.10 | 0.08 [1.81, 1.78] | 0.08 [1.73, 2.30] | 0.07 [1.63, 2.93] | 0.07 [1.57, 3.72] | 0.07 [1.56, 4.63] | 0.07 [1.54, 5.74] |
0.15 | 0.08 [2.40, 2.01] | 0.07 [2.25, 2.56] | 0.07 [2.07, 3.18] | 0.07 [1.96, 4.04] | 0.06 [1.97, 5.04] | 0.05 [1.96, 6.45] |
0.20 | 0.07 [3.71, 2.23] | 0.06 [3.24, 2.92] | 0.06 [2.93, 3.60] | 0.05 [2.79, 4.41] | 0.04 [2.66, 5.61] | 0.03 [2.67, 7.25] |
0.25 | 0.06 [5.04, 2.40] | 0.06 [4.10, 2.96] | 0.05 [3.67, 3.81] | 0.04 [3.40, 4.82] | 0.03 [3.25, 6.05] | 0.02 [3.22, 7.58] |
0.30 | 0.06 [6.99, 2.66] | 0.05 [5.30, 3.22] | 0.04 [4.73, 4.20] | 0.03 [4.28, 5.36] | 0.02 [4.11, 6.62] | 0.01 [4.04, 8.17] |
Outcome effect(remediation) | Selection effect (s = p_{1∙}–p_{2∙}) | |||||
---|---|---|---|---|---|---|
(r = p_{21}–p_{22}) | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 |
0.05 | −0.05 [1.24, 1.30] | −0.05 [1.21, 1.69] | −0.05 [1.19, 2.12] | −0.04 [1.18, 2.62] | −0.04 [1.18, 3.22] | −0.04 [1.17, 3.96] |
0.10 | −0.05 [1.64, 1.23] | −0.05 [1.55, 1.59] | −0.04 [1.49, 2.01] | −0.04 [1.46, 2.51] | −0.03 [1.44, 3.10] | −0.03 [1.44, 3.77] |
0.15 | −0.05 [2.31, 1.19] | −0.05 [2.08, 1.54] | −0.04 [1.96, 1.96] | −0.03 [1.89, 2.45] | −0.03 [1.86, 3.00] | −0.02[1.83, 3.69] |
0.20 | −0.05[2.93, 1.16] | −0.04[2.56, 1.51] | −0.04[2.36, 1.91] | −0.03[2.24, 2.40] | −0.02[2.18, 2.95] | −0.01 [2.17, 3.62] |
0.25 | −0.05[4.11, 1.08] | −0.04[3.42, 1.43] | −0.03[3.03, 1.82] | −0.02[2.83, 2.28] | −0.01 [2.71, 2.84] | 0.00 [2.68, 3.47] |
0.30 | −0.05[6.46, 1.05] | −0.04[4.83, 1.38] | −0.03[4.13, 1.77] | −0.02[3.71, 2.24] | −0.01 [3.53, 2.76] | 0.00 [3.46, 3.38] |
Calibrated confounders | First-year GPA | Remediation |
---|---|---|
Parental education (post-BA) | 0.10[1.57, 1.45] | −0.05[1.92, 1.44] |
SAT score (1,270) | 0.08[4.71, 1.93] | −0.04[9.56, 1.89] |
HS calculus course-taking | 0.07[2.66, 2.04] | −0.03[4.37, 2.04] |
Within each cell of the two-by-two table, I report simulated estimates of dual enrollment based on properties of U. Results in bold represent statistically significant effects and values in brackets represent the outcome effect (Γ) and selection effect (Λ), respectively, of U as odds ratio. I further calibrate U to exert an influence on dual enrollment and the outcome similar to parental education (post-bachelor’s), SAT scores (1,270 or higher), and math coursework in high school (calculus). I use a 1,270 SAT score to denote the average SAT score of a typical prospective student for a highly competitive college or university (Barron’s Educational Series 2002). These students scored in the 91st percentile or higher on their SATs for the BPS:04/09 sample. It is important to keep in mind that I do not remove these confounders from the selection equation but rather that I give U an association that behaves similarly to the observed covariate. By calibrating U to a known (and important) covariate, readers are able to gauge the seriousness a potential unobserved confounder is in relation to the estimate.^{2}
I reverse code whether a student participated in a remedial course because the sensitivity analysis requires positive selection. Positive selection decreases positive results, but increases negative findings. In order to assess the extent to which hidden bias drives the results to zero, I need to reverse code negative estimates. I code these estimates back, so that a negative estimate represents a “positive” program effect, after the sensitivity analysis. However, I do not convert back outcome and selection effects of U, which are expressed as odds ratios, because I want to maintain uniformity across outcomes (which has both positive and negative estimates) and readers may not recall that some odds ratios less than one (e.g., θ_{x1} = 0.2) is a stronger effect than some odds ratios greater than one (e.g., θ_{x1} = 2). Readers simply take the inverse of the odds ratio in order to obtain correct outcome and selection effects of U, as it pertains to negative estimates.
Results show that U would need to exert a large influence to undermine the positive effect of dual enrollment on first-year GPA. All things being equal, if U takes an association similar to parental education (post-bachelor’s degree), then U increases the odds of participating in dual enrollment by 45 % (Λ = 1.45) and increases the odds of earning an above-average GPA by 57 % (Γ = 1.57). Despite an unobserved confounder as strong as parental education, the dual enrollment effect remains statistically significant (0.10). Among the three observed covariates I use to anchor U, calculus course-taking generally exerts the largest influence on the estimated coefficient. Calibrating U to have an association similar to calculus course-taking, students with positive U are 2.04 times as likely in their odds to participate in dual enrollment and 2.66 times as likely in their odds to earn an above-average GPA as students without U. This leads to a 34 % reduction in the program effect, from 0.11 to 0.07, in a CIA violation of this magnitude. Despite this reduction, the dual enrollment effect does not disappear.
At what point does the effect of dual enrollment on first-year GPA no longer statistically significant due to U? If U exerted a similar outcome effect as taking calculus in high school on college GPA (r ≈ 0.20 or Γ ≈ 2.67), for example, then U would need to exert a selection effect that is about 2.8 times as large as calculus course-taking (ln(7.25)/ln(2.04); denominator is the selection effect for U calibrated as calculus course-taking) in order to reduce the estimate to statistical insignificance. For a more balanced confounder, such that U exerts a selection effect of 5.36 (s = 0.20) and an outcome effect of 4.28 (r = 0.30), U would affect the outcome slightly weaker than an SAT score of at least 1270 but would require a selection effect that is about 2.6 times as large as SAT (ln(5.36)/ln(1.93)).
The effect of dual enrollment on remediation breaks down somewhat faster than GPA to violations of CIA, although I still require a strong unobserved confounder to undermine the results. In general, U would need to exert an influence on selection into dual enrollment and remediation that is similar to calculus course-taking. Overall, the sensitivity analysis shows that results are robust to strong unobserved confounders that positively affect both selection and outcome. For remediation, I require a confounder as strong as calculus course-taking to undermine the result. For first-year GPA, I require an even larger confounder to drive the result to statistical insignificance.
Differential Effects of Dual Enrollment by SES
Returning to panel B of Table 1, I report results that show SES differences in the influence of dual enrollment on academic performance and college readiness. For simplicity, I use parental education as a measure of SES, which typically comprise of parental education, parental occupation, and family income (Hauser et al. 1983). The BPS:04/09 data set does not contain necessary indicators, in particular a measure of parental occupation, to create a composite measure of SES. Social scientists further find that each SES indicator exerts different influences on measures of social standing (Hauser 1972). In this study, I find that parental education exerts a stronger influence on dual enrollment participation than family income.
Overall, dual enrollment participants whose parents did not earn a bachelor’s degree perform better in college than nonparticipants. Among students with parents who did not attend college (e.g., first-generation students), for example, students who participated in dual enrollment earned a GPA that is 0.09 points higher than comparable students who did not participate in dual enrollment. Furthermore, the proportion of these students who take a remedial course is 4 percentage-points lower if they participated in dual enrollment than not, although the estimated coefficient is marginally significant (p < 0.10). I find similar results for students whose parents attended college but did not earn a bachelor’s degree. I find little evidence that the influence of dual enrollment on academic performance and college readiness differs across levels of parental education. Although there are differential effects of dual enrollment by parental education, in terms of absolute magnitude, these differences are not statistically significant. Despite this finding, the important result is that first-generation students who participated in dual enrollment tend to perform better in college than nonparticipants.
Does Dual Enrollment Reduce Parental-Education Gaps in Academic Performance and College Readiness?
Thus far, I showed that students who participated in dual enrollment, on average, performed better in college than students who did not participate in dual enrollment. Moreover, I showed that benefits of dual enrollment are not relegated solely to students with college-educated parents; first-generation students also benefit from dual enrollment. The question remains, however, whether unequal participation in dual enrollment by parental education contributes to parental-education gaps in academic performance and college readiness. Prior research showed that low-SES students are less likely to participate in dual enrollment than mid- and high-SES students (Meade and Hofmann 2007). It stands to reason, therefore, that differences in high school course participation by parental education account partly for parental-education gaps in academic performance and college readiness (Dual enrollment in Texas 2010; Hoffman et al. 2008).
To address this question, I partition differences in first-year GPA and remediation by parental education. For first-year GPA, a continuous variable, I perform Blinder–Oaxaca decomposition (Jann 2008) where parental education differences in the expected values of first-year GPA are due to group differences in the distribution of covariates (i.e., the endowment effect) and due to differential effects of covariates (i.e., the coefficient effect). In addition, I examine the portion in which dual enrollment accounts for the endowment and coefficient effect. I further report results for academic achievement and math coursework as these factors exert substantial contributions to college success. I suppress results from other covariates, but include them in the decomposition, as they do not relate directly to my research questions (but make available these results upon request).
For remediation, I use Breen et al.’s (2011) decomposition approach, which allows me to conduct decomposition analysis on models with dichotomous outcomes. I decompose average partial effects of parental education on remediation into its direct and indirect parts. I perform a simple decomposition analysis where dual enrollment mediates the relation between parental education and remediation. I then control for academic achievement and math coursework, as well as, the full array of covariates from the selection equation as possible confounders to the decomposition analysis.
Blinder–Oaxaca decomposition of parental-education differences in first-year GPA (first-generation students are reference category)
GPA | |||
---|---|---|---|
Some college | Bachelor’s degree | Post bachelor’s | |
Endowment effects | |||
Difference | 0.11*** (0.02) | 0.30*** (0.02) | 0.41*** (0.02) |
Total | 0.08*** (0.01) 74.0 % | 0.24*** (0.01) 81.0 % | 0.33*** (0.02) 81.2 % |
Select covariates | |||
Dual enrollment | 0.004** (0.001) 3.6 % | 0.003* (0.002) 1.1 % | 0.01** (0.002) 1.9 % |
SAT scores | 0.06*** (0.01) 53.8 % | 0.14*** (0.01) 45.8 % | 0.18*** (0.02) 45.0 % |
HS GPA | 0.02*** (0.004) 17.8 % | 0.06*** (0.01) 19.9 % | 0.08*** (0.01) 19.5 % |
Math coursework | 0.01*** (0.003) 10.3 % | 0.04*** (0.01) 12.6 % | 0.05*** (0.01) 13.1 % |
Coefficient effects | |||
Total | 0.03 (0.02) 26.0 % | 0.06** (0.02) 19.0 % | 0.08** (0.03) 18.8 % |
Select covariates | |||
Dual enrollment | 0.01 (0.01) 5.8 % | −0.01 (0.01) −2.8 % | −0.001 (0.01) −0.2 % |
SAT scores | 0.14 (0.16) 124.6 % | 0.02 (0.17) 6.4 % | −0.10 (0.19) −23.8 % |
HS GPA | 0.21 (0.15) 187.5 % | 0.33 (0.15) 110.0 % | 0.41^{†} (0.24) 101.4 % |
Math coursework | −0.02 (0.03) −20.8 % | −0.03 (0.04) −9.5 % | −0.01 (0.06) −1.3 % |
Academic achievement accounts for the lion’s share of the parental-education gap in first-year GPA. For example, almost half of the gap in first-year GPA between first-generation students and students with a parent who earned a bachelor’s degree is due to differences in the distribution of SAT scores where first-generation students, on average, are at the lower end of the distribution than students with college-educated parents.
Total, direct, and indirect effects of parental education on remediation
Remediation | |||
---|---|---|---|
Col. A | Col. B | Col. C | |
Some college | |||
Total effect (S.E.) | −0.05*** (0.01) | 0.01 (0.01) | 0.01 (0.01) |
Direct (S.E.) | −0.05*** (0.01) | 0.01 (0.01) | 0.01 (0.01) |
Dual enrollment (S.E.) % reduced | −0.01*** (0.001) | −0.001^{†} (0.0003) | −0.001^{†} (0.0003) |
9.6 % | −6.4 % | −7.5 % | |
Bachelor’s degree | |||
Total effect (S.E.) | −0.15*** (0.01) | 0.002 (0.01) | 0.01 (0.01) |
Direct (S.E.) | −0.15*** (0.01) | 0.003 (0.01) | 0.01 (0.01) |
Dual enrollment (S.E.) % reduced | −0.01*** (0.001) | −0.0002 (0.0003) | −0.0002 (0.0003) |
4.9 % | −9.6 % | −2.8 % | |
Post-bachelor’s | |||
Total effect (S.E.) | −0.24*** (0.01) | −0.02* (0.01) | −0.01 (0.01) |
Direct (S.E.) | −0.22*** (0.01) | −0.02* (0.01) | −0.01 (0.01) |
Dual enrollment % reduced | −0.01*** (0.002) | −0.001* (0.0004) | −0.001* (0.0004) |
5.4 % | 3.8 % | 6.6 % |
Similar to results of first-year GPA, dual enrollment accounts for a modest portion—between 5 % and 10 %—of the parental-education gap in remediation (see “% reduced” in col. A). For example, dual enrollment accounts for about 10 % of the remediation gap between first-generation students and students with a parent who attended college but did not attain a bachelor’s degree. These results imply that the parental-education gap in remediation is minimally due to differences in dual enrollment participation.
Instead, the parental-education gap in remediation is largely due to differences in student background characteristics. In particular, the direct effect of parental education on remediation reduces considerably after I include SAT scores, high school GPA, and math coursework (see “col. B”). For example, controlling for academic achievement and coursework fully accounts for the gap in remediation between first-generation students and students with at least one parent who went to college. The exception is the parental-education gap between first-generation students and those with a parent who attained a post-bachelor’s degree, although student differences in academic achievement and coursework reduce the gap by 90 %, from 24 percentage points in col. A to 2 percentage points in col. B. However, this gap is eliminated after I control for the full array of covariates from the selection equation. These results suggest that reducing gaps in academic performance and college readiness between first-generation students and students with college-educated parents would require more than equalizing dual enrollment participation. Perhaps not surprisingly, students bring different background characteristics when they enter dual enrollment programs and they leave these programs at different places in the college-preparatory distribution as well.
Conclusion
With most adults obtaining at least a high school diploma, the importance of future well-being increasingly depends on whether individuals participate in postsecondary education (Ashenfelter and Rouse 1998). As college-degree attainment becomes the prerequisite for an adequate standard of living, discussions of college access and persistence, especially among low-SES students, has remained a priority among researchers, educators, and policy makers. The SES gap in educational attainment has remained stable in the 1980s, but the increasing rates of high school graduation shifted the importance of SES inequalities away from high school and toward college (and pre-school) levels (Mare 1995).
Given the decline in the purchasing power of need-based aid (e.g., Pell Grants) and the rise of merit-based aid, policy makers seek alternative means, such as dual enrollment, to increase college access and improve college success for low-SES students (Haveman and Smeeding 2006; Hoffman 2007). Dual enrollment advocates argue that these programs better prepare students for college coursework than a traditional high school program. However, research on the effects of dual enrollment is in its early stages (Bailey et al. 2002; Karp et al. 2007). Despite this lack of research, policy makers are pushing forward and proposing a larger implementation of these programs that would reach a wider range of students. It is therefore important to examine effects of dual enrollment on academic performance and college readiness, and whether these effects equally benefit all students or for only students with college-educated parents, for example.
I had four goals for this study. The first goal was to estimate effects of dual enrollment that account for potential confounding factors that affect both selection and outcome. Using propensity score matching models, I found that dual enrollment continues to influence positively academic performance and college readiness. I found that the influence of dual enrollment on first-year GPA is similar, albeit smaller, than previous studies (Allen and Dadgar 2012; Karp 2007; Morrison 2007). On average, first-year GPA was 0.11 points higher for dual enrollment participants than for nonparticipants. Furthermore, dual enrollees were less likely to participate in remediation than non-dual enrollees, which is also consistent with past research (Kim and Bragg 2008).
Although I found statistically significant results, readers may wonder whether these results are substantively significant. The extent to which dual enrollment exerts a significant effect depends, in part, on how readers interpret the magnitude of the effect. In this study, the effect size of dual enrollment on first-year GPA was 0.13. Although similar in magnitude to previous studies (e.g., Allen and Dadgar 2012; Karp 2007), it is unclear the importance of this effect. One way to assess its importance is to compare the magnitude of dual enrollment on GPA to other important gaps in academic performance. For example, the effect size of dual enrollment on first-year GPA is similar in magnitude to SES and gender. (Allen et al. 2008), as well as, to the black–white gap in first-year GPA at private and selective schools (Turley and Wodtke 2010; Wolniak and Engberg 2010). Future research should continue to develop standards for which researchers can evaluate the substantive importance of dual enrollment on postsecondary schooling. Although these approaches account for a host of important observed covariates, unobserved indicators that affect both selection into dual enrollment and the outcome may continue to drive results.
The second goal was to test the sensitivity of results to potential unobserved confounders. I found that the influence of dual enrollment on first-year GPA and remediation were resilient to moderate and even major violations of CIA. The sensitivity analysis of estimates from the propensity score matching model showed that an unobserved confounder would have to be as large as high school calculus course-taking—and even larger for first-year GPA—to undermine the relation between dual enrollment and remediation. Although I found an overall effect of dual enrollment, it was not immediately clear whether this result masked heterogeneous effects across the SES spectrum. First-generation students are underrepresented in dual enrollment than students with college-educated parents, and as a consequence, proponents of dual enrollment advocate for increasing program access in order to improve college preparation.
The third goal was to estimate academic gains of dual enrollment across levels of parental education. I found that dual enrollment did not hinder academic performance and college readiness for first-generation students. In general, the influence of dual enrollment was uniform across levels of parental education. These results suggest that dual enrollment serves as an effective means to raise academic preparation for a wider range of students than these programs originally intended. Although increasing dual enrollment participation may increase academic performance and college readiness for students, this increase does not necessarily translate to a reduction in academic gaps between first-generation and non-first-generation college students.
The fourth goal was to evaluate whether dual enrollment reduces parental-education gaps. I found little evidence that a general expansion of dual enrollment participation would reduce parental-education gaps in first-year GPA and remediation. Less than 4 % of the parental-education gap in first-year GPA is attributable to differences in dual enrollment participation. Similarly, between 5 % and 10 % of the parental-education gap in remediation is due to differences in dual enrollment participation. The contribution of dual enrollment participation in the parental-education gap is almost entirely due to differences in academic achievement and coursework between first-generation students and students with college-educated parents. Therefore, although first-generation students benefit from dual enrollment as much as non-first-generation students, parental-education gaps remain because of baseline differences between first-generation and non-first-generation students, even among those who participated in dual enrollment.
Dual enrollment proponents may confound effects of dual enrollment on academic achievement and college readiness with schooling outcomes of dual enrollees. The situation in which students from different family backgrounds produce similar schooling outcomes and experience a uniform dual enrollment effect is when all students who participate in dual enrollment are similar in their baseline characteristics. What prior studies are generally silent about, however, is that students—even among those who participated in dual enrollment—may enter these programs with baseline differences but also leave these programs with these differences. Using academic preparation as an example, low-SES students may occupy the lower half of the distribution relative to other dual enrollees, whereas high-SES students may occupy the upper half of the distribution. As a consequence, even if all students experienced similar effects of dual enrollment on academic performance and college readiness, these programs may not close the parental-education gap. We would therefore require greater efforts that move beyond equal participation of dual enrollment, and instead concentrate on targeting low-income schools to reduce further parental-education gaps.
Limitations of Study and Future Research
Although this study provides insight to the influence of dual enrollment on academic performance and college readiness, this study is limited in five ways. First, the data do not allow me to disentangle varying effects of delivery in dual enrollment programs on academic performance and college readiness. High school districts may provide dual enrollment on a college campus, at the high school, or online (Blackboard Institute 2010). Each mode of delivery has its advantages but it also has its drawbacks. Some researchers argue that dual enrollment on a college campus provides the maximum benefits of dual enrollment because, although dual enrollment programs—regardless of delivery—teach college courses (Blackboard Institute 2010), on-campus instruction provides the added benefit of a college experience (Burns and Lewis 2000; Karp 2007). These results potentially overestimate effects for some types of dual enrollment while underestimate effects for other types. The research agenda would benefit from researchers examining varying effects of dual enrollment by mode of delivery.
A second limitation is that the data do not allow me to explore “dosage” effects of dual enrollment. The influence of dual enrollment may differ based on the number of dual enrollment courses in which a student participates. A third limitation is that I am unable to assess effects of subject-content in dual enrollment courses on academic performance and college readiness. Future research that considers the number of dual enrollment courses in which students participate, as well as, the subject content of the course would advance our understanding of the influence of dual enrollment on postsecondary schooling.
A fourth limitation is whether propensity score matching models provide an advantage over other approaches, such as multiple regression. Some researchers are skeptical that propensity score matching produces results that are better than results from multiple regression (Angrist and Pischke 2009; Padgett et al. 2010). I do not wish to debate the benefits of propensity score matching over multiple regression but instead state that I used propensity score matching models because it allowed me to take advantage of developments in sensitivity analysis over the past 30 years (Ichino et al. 2008; Rosenbaum 1987; Rosenbaum and Rubin 1983). The sensitivity analysis that I used allowed me to manipulate the magnitude of a simulated unobserved confounder in its influence on both selection and outcome.
A fifth limitation is that although I found that results are resilient to potentially large unobserved confounders, these results do not imply that hidden bias cannot undermine results. Although BPS:04/09 contains a rich set of variables that influence dual enrollment participation, this data set is limited in its collection of indicators that capture in-depth relations between high school students and their environment, such as parent–child interactions, peer influences, and high school contextual factors. To assess partly consequences of this limitation, I conducted supplemental analyses with data from the National Education Longitudinal Study of 1988 (NELS:88). Although NELS:88 contain an older cohort of students than BPS:04/09, NELS:88 contains a richer set of pre-college covariates (e.g., parent–child discussions and high school context measures) than BPS:04/09. I further conducted endogenous switching regression to supplement the sensitivity analysis. The advantage of endogenous switching regression is that this approach jointly estimates the correlation in errors between program assignment (e.g., dual enrollment) and outcome. This approach estimates the degree to which common, unobserved confounders affect both program assignment and outcome (Mare and Winship 1988). I found that results from supplemental analyses did not change the substantive conclusions of the propensity score matching model and sensitivity analysis (results available upon request). However, continued efforts that capture the selection process of dual enrollment are needed in order to understand better family, peer, and school influences that affect dual enrollment participation.
I performed covariate imbalance tests to examine whether the propensity score successfully balanced the distribution of covariates across program conditions (results not shown). I calculated the standardized bias before and after matching. Prior to matching, the average bias across all covariates between dual enrollment participants and nonparticipants was 14.4 %. I found a 76 % reduction in bias after matching where the average bias is 3.5 %.
Following convention (Ichino et al. 2008), I fix parameters Pr(U−1) and p_{11}−p_{12} to predetermined values in order to reduce the dimensionality in the characterization of U. The parameter Pr(U = 1) represents the proportion of individuals with U in the sample, while p_{11}–p_{12} represents the effect of U on the outcome among the treated. Because the concern is that the control group may not produce an unbiased estimate of the counterfactual outcome of the treated, I am able to fix these parameters and fully characterize U through the manipulation of (r = p_{21}–p_{22}) and (s = p_{1∙}–p_{2∙}) (Ichino et al. 2008).
Acknowledgments
The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Award #R305B090009 to the University of Wisconsin-Madison. The opinions expressed are those of the author and do not represent views of the U.S. Department of Education. I am grateful to Adam Gamoran, Markus Gangl, Ted Gerber, Sara Goldrick-Rab, and two anonymous reviewers for helpful comments on earlier drafts.