Abstract
We study the effects of access to high school math and science courses on postsecondary science, technology, engineering, and mathematics (STEM) enrollment and degree attainment using administrative data from Missouri. Our data include more than 140,000 students from 14 cohorts entering the 4-year public university system. The effects of high school course access are identified by exploiting plausibly exogenous variation in course offerings within high schools over time. We find that differential access to high school courses does not affect postsecondary STEM enrollment or degree attainment. Our null results are estimated precisely enough to rule out moderate impacts.
Keywords
Introduction
Improved access to STEM courses in high school has been advocated as a lever by which the STEM workforce can be expanded and diversified. The idea is that exposure to more, and more advanced, STEM courses in high school will lead to more interest and success in STEM in college, which, in turn, will translate to a more robust STEM workforce. Calls for improved access to STEM coursework in high school—especially in schools that primarily serve underrepresented minorities—have come from policy and advocacy groups, journalists, and the highest levels of government. For example, the Obama Administration’s “STEM for All” campaign argued that For high-school students, access to core and advanced STEM coursework is an essential part of preparing to enter the workforce equipped with relevant skills for a broad range of jobs, and to successfully pursue STEM degrees and courses in college. (White House, 2016)
1
Although there are reasons to believe that the “STEM crisis” in the United States is overstated (Berliner & Glass, 2014), the broad policy push to expand on and improve STEM education in the United States remains strong. 2
We use administrative data from Missouri tracking more than 140,000 students who matriculate into the statewide 4-year public university system over a 14-year period to study the effects of access to STEM coursework in high school on STEM enrollment and degree completion in college. Our research design aims to assess the potential for expansions in access to the “business as usual” STEM courses that high schools already offer to lead to better postsecondary STEM outcomes. This stands in contrast to studies of smaller scale programs and interventions designed to increase STEM or other course-taking behaviors in high schools, which often come with external resources and incentives (e.g., Jackson, 2010, 2014). 3 Our focus on understanding the effects of natural variation in already-available high school courses is useful if the goal is to affect STEM preparation and training at scale in the near term, in which case, policy responses within the boundaries of what schools are already doing are appealing.
We build on a large academic literature devoted to studying the relationship between STEM course-taking in high school and STEM outcomes in college. A well-established empirical regularity from this literature is that the more STEM courses a student takes during high school, the higher her likelihood of STEM enrollment and degree attainment in college (e.g., see Maltese & Tai, 2011; Sadler & Tai, 2007; Wang, 2013). However, the endogeneity of students’ own course-taking behaviors makes causal inference from this finding difficult—unobserved preference or endowment heterogeneity likely lead to both the pursuit of technical courses in high school and college STEM outcomes.
To improve causal inference, we build methodologically on a related literature on the effects of high school curricula more broadly. From a methodological perspective, our work follows most closely on studies by Altonji (1995), Levine and Zimmerman (1995), and Rose and Betts (2004). Like in our study, these authors leverage variation in course availability for identification in recognition of the endogeneity concern with students’ own course-taking behaviors. But although helpful, this does not fully resolve the endogeneity problem because of the well-understood concern that course offerings at a high school may be related to student sorting to schools, and possibly other resources and opportunities, which can also affect college outcomes. Previous studies were unable to address the school-level endogeneity issue because they rely on cross-sectional data. An innovation of our study is the construction of a 14-year data set of entrants into Missouri’s 4-year public university system, merged with administrative records on course offerings at the high school level. 4 This facilitates a high school fixed-effects identification strategy that leverages variation within high schools over time in course offerings, allowing us to address both the individual- and school-level endogeneity threats.
Our within-high-school identification strategy improves on the methodology of previous studies but raises two issues. First, we sacrifice statistical power by relying entirely on within-high-school variance for identification. However, this concern is of limited practical importance in our study because of our large sample and the nonnegligible within-high-school variance share of course offerings. 5 The second issue is the potential for endogenous changes in course offerings within high schools over time. Over the full 14 years of our data, such changes seem plausible—for example, a compositional shift in a neighborhood might induce a change in the high school curriculum driven by shifting student interests. However, over shorter time intervals, variation in course offerings within a high school is more likely to be driven by idiosyncratic shocks. Examples include changes to personnel and rigidities in the functions that map course offerings to enrollment (i.e., rules, implicit or explicit, governing how many sections of a course are offered based on projected enrollment and class sizes). Although we lack data on the programmatic details that drive curriculum changes to isolate specific channels, we test indirectly for evidence of bias from endogenous changes within high schools over time by partitioning our data set into a series of shorter time periods. Over the shorter time periods, systematic, endogenous shifts within high schools are less likely. This exercise provides no indication that our findings are biased by this type of endogeneity.
We find that expanded access to STEM courses in high school does not increase postsecondary STEM enrollment or degree attainment. Our estimates are substantively small and precise. Point estimates from our preferred models imply effect sizes of a one standard deviation increase in high school course access on postsecondary STEM enrollment and attainment of just 0.10 to 0.15 percentage points. With 95% confidence, we can rule out effects larger than 3% to 5% of the sample means for these outcomes. Our null findings are robust to numerous measurement modifications. They persist if we separately estimate the effects of access to math and science courses, and access to math courses that differ by the content level (regular or advanced).
We also show that there is no detectable effect heterogeneity across high schools that differ by the racial/ethnic minority share of the student body. Policy proposals to expand STEM course access at high schools with high minority shares reflect the concern that a lack of access affects students who attend these schools specifically. However, our results give no indication that access to courses is the problem. There is evidence of modest effect heterogeneity by gender and race within high schools, but the heterogeneity is not in a direction that suggests increases in course access will reduce postsecondary STEM outcome gaps—male and White students are marginally more responsive to changes in course access relative to women and underrepresented minority students. On the whole, these results indicate that simply increasing the number of math and science courses offered in high school is unlikely to change the demographic distribution of college STEM degrees in the direction intended by policy.
Finally, as a complement to our analysis of course access, we explore models that aim to identify the causal effect of course-taking in high school. These models use course access as an instrument for courses taken by students. The instrumental variables (IV) models are ultimately uninformative about the effect of course-taking, but the reason provides insight into our null findings for course access. Specifically, the first-stage regressions show that although increases in course access correspond positively to increases in course-taking, the mapping is substantively weak. The weak link between course access and course-taking, which is presumably the first-order pathway by which increased access would affect postsecondary STEM outcomes, is not consistent with the presence of widespread excess demand for math and science courses in high school. 6 In the “Conclusion” section, we discuss the implications of our findings for policy moving forward.
Empirical Approach
We build on the methodological structure used by Altonji (1995), Levine and Zimmerman (1995), and Rose and Betts (2004). First, consider the following cross-sectional linear regression linking student course-taking in high school to subsequent outcomes:
In our application,
We would like to interpret
We address the first issue by substituting a measure of the courses offered by the high school for actual courses taken by each student:
Equation 2 is the same as Equation 1 except for the substitution of
The advantage of the model in Equation 2 is that CAs does not incorporate variation from student i’s own course-taking behavior to identify
Although identification is improved in Equation 2 relative to Equation 1, Equation 2 relies on variation across high schools in course offerings for identification. Altonji (1995), Levine and Zimmerman (1995), and Rose and Betts (2004) recognized this limitation but had access only to cross-sectional data and, thus, were unable to address it fully. A straightforward but important innovation of our study is the construction of a long data panel of high schools, which allows for an improved methodological approach (as advocated by Altonji, Blom, & Meghir, 2012). Specifically, our preferred models are panel-data versions of Equation 2 that leverage our ability to observe multiple cohorts of students graduating from high schools over time:
Equation 3 builds on Equation 2 with the addition of a time dimension, indexed for cohorts of high school graduates by t. Correspondingly, we can include high school and year fixed effects in the model,
The concern that endogenous course offerings across high schools will bias the results is mitigated by Equation 3. As noted previously, the remaining threat to identification is endogenous changes to course offerings within high schools over time. Below, we show results from a test designed to detect bias from such changes and we do not find evidence of bias. Equation 3 is our preferred specification for estimating the causal effects of access to STEM courses in high school.
In addition to the policy relevance of our reduced-form ITT parameter,
Still, models that aim to identify the direct effect of course-taking are also of interest. By imposing more restrictive assumptions on the causal pathway, we can recover treatment effects of course-taking using an IV approach (Wooldridge, 2002). The IV approach uses variation in course offerings within a high school over time to instrument for courses taken by students, and, in turn, use the instrumented values to estimate the effects of courses taken, as follows:
To support a causal interpretation,
The first stage of the IV model also proves useful for contextualizing our findings. As we show below, exposure to additional STEM courses in high school is a statistically significant predictor of the number of STEM courses taken. However, the substantive mapping of course exposure to course-taking is weak. The weak link between course access and course-taking helps to explain our primary finding that access to more STEM courses in high school does not improve STEM outcomes in college.
Background
Data and Context
Our student records are from administrative data provided by the Missouri Department of Higher Education (DHE). We focus on full-time, first-time students who graduated from a Missouri public high school and matriculated to a 4-year Missouri public university within 2 years of completing high school. Our data cover more than 140,000 students from 14 cohorts of entrants into the public university system between 1996 and 2009.
There are 13 public 4-year universities in Missouri as listed in Supplemental Table S2, available in the online version of the journal. STEM education is highly concentrated within the system, with nearly 60% of STEM graduates coming from just two universities: the state flagship University of Missouri-Columbia (37% of all STEM graduates) and the engineering-focused Missouri University of Science and Technology (22% of all STEM graduates, despite accounting for just 4% of system enrollees). Three other universities—the highly selective Truman State University and moderately selective Missouri State University and University of Central Missouri—produce 6% to 8% of STEM graduates each; all other universities produce 5% or fewer of STEM graduates. 9
We track each student in the Missouri system to determine whether she graduated within 6 years of entry (from any system school), and if so, her final major. 10 The DHE data also include detailed information about students’ academic ability that we incorporate into our models—that is, ACT math and English scores (following Bettinger, Evans, & Pope, 2013) and high school class ranks. Moreover, the number of courses students take in each of several subjects during high school, including math and science, are taken from the DHE data. A “course” is defined as 1 year of course-taking. During our analysis period, students needed to complete two math courses and two science courses to meet minimum high school graduation requirements established by the State Board of Education. 11 For students who intend to enroll in a public university in Missouri, the Coordinating Board for Higher Education (CBHE) recommended four mathematics courses.
We code initial majors and degrees based on the Classification of Instructional Programs (CIP) taxonomy developed by the U.S. Department of Education for college majors. The initial major is an “intended” major; there are no requirements or formal system rules that govern the initial selection. We classify each major as either STEM or non-STEM, with STEM including the following fields: engineering (7% of initial majors), biological science (6%), computer science (3%), physical science (2%), engineering technology (1%), agricultural and animal science (1%), mathematics (1%), and other STEM (1%). Our classification of STEM majors is based on the National Science Foundation’s (NSF) definition—the online Supplemental Appendix B provides details. 12
Figure 1 shows trends in STEM majors and degrees for the entering cohorts in our sample from 1996 to 2009. Initial interest in STEM remained relatively flat over most of the time period but increased in the later years; in total, initial STEM enrollment increased 20%, or roughly 5 percentage points, between 1996 and 2009. Similarly, STEM attainment increased by about 23%. The growth in women declaring STEM majors was similar to the overall rate, but the growth in attainment among women was slightly below the sample average. The trend in initial STEM enrollment among underrepresented minority students (defined here as Black and Hispanic students) is noisier but grew at a similar rate to the overall trend. However, STEM degree attainment declined by 13% among these students.
Trends in STEM initial major and degrees by HS Cohort: (a) initial major and (b) degree, among all entrants.
We supplement the DHE data with a database on high school course offerings that we assembled using administrative records from the Missouri DESE. DESE assigns a topical designation for each course number in the system. We use DESE’s designations to identify high school math and science courses. DESE defines a “course” as equivalent to 1 year of instruction and we follow this convention here. 13
In our preferred measure of course availability, each course offering is treated as a separate course. For example, if a high school has three Algebra I offerings in a single year, this counts as three math courses. We also adjust by high school enrollment to get measures of “courses available per 100 students.”
Our course-availability measures aim to capture the average exposure of students to STEM courses during the high school career. For each student in each cohort at each high school, we use the 3-year average of the total number of (enrollment adjusted) courses offered during the student’s graduation year, and the 2 years prior (we use 3 years because some high schools span Grades 9–12 and others span Grades 10–12). A one-unit increase in our measure indicates that, on average, the student was exposed to one additional STEM course per year per 100 students during Grades 10 to 12, or alternatively, the student was exposed to three additional courses per 100 students in total during Grades 10 to 12. 14
Figure 2 shows trends over time in access to high school STEM courses in Missouri. The black solid line represents all math and science courses available per 100 students—the trend is relatively flat, with a slight uptick by the end of the period (overall growth of about 6% from 1996 to 2009). We also separately plot advanced math, high school–level math, and science courses. Dividing math and science courses is straightforward based on the DESE course codes; to differentiate the content of math courses, we coded each math course as either “advanced” (i.e., college prep and college-level courses) or “standard” (i.e., high school–level math courses) based on the course title in the administrative records (we were unable to follow a similar process to classify science courses because of inconsistent reporting across high schools and years). 15 The overall growth in math and science courses is driven primarily by increases in advanced math offerings, with the average advanced math offering increasing nearly 14%. Over the analysis period, standard high school–level math course access stayed flat, whereas average science course access declined by about 7%.
Trends in high school STEM course access by HS cohort.
In sensitivity checks, we also use two other measures of course availability. The first is the total number of course offerings unadjusted for student enrollment. A larger number of course offerings may provide more access in an absolute sense, in a way that is missed by our enrollment-adjusted measures. The second is a measure of “topic availability,” which we also measure per 100 students. The “topic availability” measure does not count each section of a course separately. For example, if a high school offers three sections of Algebra I in a single year, this counts as just one topic. The value of this alternative measure is best articulated by noting that our primary measure captures variation in access to STEM courses along two dimensions: (a) increased availability of seats holding the topic set fixed and (b) increased availability of topics. The topic availability measure isolates variation along the latter dimension only.
We additionally collect data on high school characteristics from the Common Core of Data made available by the National Center for Educational Statistics (NCES). We merge the information about high schools to student records in the DHE data by high school and year. 16 The final merged data set includes more than 140,000 students who attended 498 public high schools and matriculated to one of the 4-year public universities in Missouri.
Summary statistics for students and high schools are reported in Table 1. The sample is 56% female and 85% White. 17 Black students comprise 8% of the sample, and Hispanic and Asian students account for 2% each. Compared with the national average, Missouri high schools are smaller in terms of enrollment and less diverse racially. High schools in Missouri are also disproportionately rural, although student representation is more balanced across high school types than is implied by the high school characteristics because rural schools are small (see columns 3 and 4).
Sample Summary Statistics
Table 2 shows that approximately 20% of initial and completed degrees at Missouri universities are in STEM fields. 18 Forty-three percent of students who declare a STEM major upon entry graduate with a STEM degree, whereas just 4% of students who do not initially declare a STEM major complete a STEM degree. These simple statistics highlight the strong link between initial STEM enrollment and completion.
STEM Initial Majors and Degrees
Source. Administrative data on Missouri public HS students who matriculate into a Missouri public 4-year university.
Note. Degree reflects degree acquisition in 6 years. STEM = science, technology, engineering, and mathematics.
Anticipated differences by race/ethnicity and gender in STEM enrollment and attainment are also displayed in Table 2. For example, the first two columns show that men are more than twice as likely as women to declare a STEM major and earn a STEM degree. Among races/ethnicities, Asian students are the most likely to initially declare a STEM major and complete a degree (31% and 21%, respectively), whereas Black students are least likely (18% and 6%, respectively). Among those who declare STEM degrees, male, White, and Asian students are more likely (46%, 44%, and 51%, respectively) than female, Black, and Hispanic students (38%, 24%, and 38%, respectively) to earn one.
Table 3 reports summary statistics on STEM course-taking and course exposure in high school. In our sample of college goers from public high schools, students take 7.1 math and science courses on average; this closely mirrors the national average of 7.0 math and science courses among public high school graduates. 19 The first takeaway from column 1 is that there is substantial variation in STEM course-taking in the data, which is measured in terms of courses that qualify for the Missouri CBHE-recommended high school curriculum. 20 About 90% of the students in our sample took between five and 11 qualifying math and science courses. 21 Columns 2 to 5 show that there is also significant variation in course availability, course availability per 100 students, and topic availability per 100 students.
Math and Science Courses Taken and Course Availability in High School
Source. Administrative data on Missouri public HS students who matriculate into a Missouri public 4-year university.
Note. Standard deviation in parentheses. All means and standard deviations are student weighted. STEM = science, technology, engineering, and mathematics.
Column 2 in row 1 shows that the average number of STEM courses available to students in our sample annually across all topics and sections is 85.2. As discussed above, the most relevant measure of STEM exposure for our empirical models is course availability per year per 100 students, which column 3 shows has an average value of 10.8. 22 The standard deviation of 3.6 gives a range of exposure within one standard deviation of the mean of 7.2 to 14.4 STEM courses per 100 students, per year, on average during Grades 10 to 12. Variation in course access within high schools over time—the variation we isolate for identification in our preferred models—accounts for 17% of the total variance of enrollment-adjusted course availability. 23
The remainder of Table 3 shows splits for the course-taking and course access measures by (a) STEM attainment status and (b) demographics. The large differences across demographic groups in terms of postsecondary STEM outcomes, shown in Table 2, are not apparent at nearly the same level when we focus on high school STEM exposure. It is the case that students who ultimately complete STEM degrees take more math and science courses in high school, but they have only a very slight advantage in course access (columns 2–5). Unsurprisingly, female and male students have similar course access (differentials would only be expected in the presence of gender segregation in high school, or substantial gendered selection into our sample from some high schools); perhaps more surprising is that female students take about the same number of math and science courses in high school as male students despite being much less likely to enroll in or complete a STEM degree in college. The splits by race/ethnicity show that Asian students take the most math and science courses relative to other groups and Black students take the least. In terms of course exposure, Black, Hispanic, and Asian students attend high schools that offer more math and science courses than White students (column 2), but this is due to the overrepresentation of White students in small, rural schools. This can be seen in column 3, where racial differences in access largely disappear when measured by courses available per 100 students. 24 There are small differences by race/ethnicity in absolute topic availability, and more pronounced differences when we adjust for enrollment. Column 5 shows that Black, Hispanic, and Asian students have fewer topics available in enrollment-adjusted terms than White students.
Tests for Effects on College Enrollment
By virtue of using students in the DHE data to define our sample, our analysis necessarily conditions on university enrollment. This means that our data are ill-suited to examine effects of STEM course access in high school on the extensive margin of college (i.e., attendance), but well-suited to examine shifts in major choice and attainment conditional on entry into the 4-year public university system. Given that individuals who initially enroll in and complete STEM majors are positively selected among high school students, the latter margin is arguably the most important. 25 Still, the potential for variation in STEM course access to affect who enrolls in Missouri 4-year public universities potentially complicates the interpretation of our estimates. 26
To get a sense of the importance of this concern, we estimate several models using DHE and supplementary data, with the results provided in the online Supplemental Table S1. In the first four columns of the table, we regress various college-going outcomes—reported at the high school by year level—on high school fixed effects and STEM course access. These regressions are aggregated to the school-by-year level but otherwise match the structure of Equation 3. The outcome variables in columns 1 to 3 are constructed from data on college matriculation rates provided by Missouri high schools, which are for all colleges (public and private) and additionally broken down by location (i.e., in state/out of state) and level (i.e., 2 years/4 years). In column 4, we use the DHE data to examine matriculation into the 4-year public university system in Missouri (i.e., into our sample). The last three columns use the same regression structure but the dependent variables are high school by year average academic qualifications of students in the DHE data. All the models are designed to test whether the composition of students in our sample is changing in response to variation in access to STEM courses in high school.
Focusing first on the matriculation regressions using the supplementary data from high schools in columns 1 to 3, there is no indication that changes to STEM course access within high schools over time affect college matriculation rates. The estimated effects on college matriculation in total, as well as matriculation to 4-year and 2-year colleges separately, are not statistically significant and the magnitudes of the effects implied by the point estimates are trivial (online Supplemental Table S1 reports the sample mean of each dependent variable for ease of interpretation). Similarly, in column 4, we do not observe an effect on the total number of students who attend a 4-year Missouri public university (the focal sample in our study).
The models of student qualifications in columns 5 to 7 corroborate the result that the composition of the students in our sample is not changing in response to changes in STEM course access during high school. Specifically, there is no indication of changes to the academic qualifications of students who matriculate into our sample as measured by ACT scores in math or English. We do observe a relationship between STEM course availability and the high school class rank, but the point estimate is very small in practical terms and on the margin of statistical significance. Specifically, the point estimate implies that a one standard deviation increase in STEM course availability per 100 students in high school corresponds to an increase in the class rank of students who matriculate into a Missouri 4-year public university of just four tenths of a percentage point, or about 0.5% of the sample mean.
Based on this analysis, we conclude that variation in the availability of high school math and science courses does not affect the composition of our sample of public 4-year college enrollees. This supports our focus on the compositional shift between STEM and non-STEM fields conditional on enrollment.
Results
Table 4 presents results from linear probability models building up to our primary specification as shown in Equation 3. 27 The outcome in the first vertical panel is an indicator variable for whether initial postsecondary enrollment is in STEM (columns 1–3) and the outcome in the second panel is an indicator for STEM degree completion (columns 4–6). Within each panel, the first row of estimates uses actual courses taken as the independent variable of interest and the second row uses courses available. We standardized courses taken and courses available to have a mean of zero and a standard deviation, so coefficients can be interpreted as standardized effect sizes. Results using our preferred specification are reported in the second row of columns 3 and 6. We suppress nonfocal coefficients for presentational convenience in the table, but full model output is provided in the online Supplemental Appendix C for interested readers (full output is available in the online Supplemental Appendix for Table 4 and all subsequent tables).
STEM Major and Degree Attainment Models
Source. Administrative data on Missouri public HS students who matriculate into a Missouri public 4-year university.
Note. Courses taken are standardized to have a mean of zero and a standard deviation of one. Course availability is courses available per 100 students, standardized to have a mean of zero and a standard deviation of one. Each coefficient is from a separate linear regression. All models control for high school graduation year (year fixed effects). Student controls are race/ethnicity and gender, ACT math and English scores, and high school class rank. High school controls include location (urban, suburban, or rural; this factor drops out with the inclusion of HS fixed effects), enrollment, percent of the student body that identifies as a minority race/ethnicity, and percent of the student body that is free or reduced price lunch eligible. Standard errors clustered by high school included in parentheses. STEM = science, technology, engineering, and mathematics; FE = fixed effects; HS = high school.
p < .05. **p < .01.
Starting with the first row of the table, we see strong relationships between courses taken and postsecondary STEM outcomes. The relationships are fairly stable across models and imply a strong link between course-taking in high school and postsecondary STEM outcomes. Recall that the baseline rates of initially choosing a STEM major and completing a STEM degree are 21% and 12% in our sample, respectively (per Table 2). The results in the top row of Table 4 are consistent with the previous literature linking STEM course-taking in high school to STEM outcomes in college (e.g., see Maltese & Tai, 2011; Sadler & Tai, 2007; Wang, 2013). However, given the concern about endogenous course selection by individual students, it is ill-advised to interpret the estimates as causal.
The second row shows results after replacing the courses-taken variable with courses available. Per above, our preferred specifications use courses per 100 students to measure access, but our findings are not qualitatively sensitive to using alternative measures (see section “Sensitivity” below). The estimates moderate substantially when we move to the models that use course access. This is attributable to two factors: (a) the removal of bias from endogenous student choices and (b) the shift in interpretation to the ITT parameter. The general takeaway reading across the columns of the second row is that the underspecified models indicate positive and sometimes statistically significant “effects” of course access in high school on postsecondary STEM outcomes. However, estimates from the full specification with high school fixed effects provide no such indication.
Although our standard errors rise some when we move to the full specification, which is expected because we leverage less identifying variation, the null results are not driven by an increase in our standard errors. The estimates themselves are quite small in magnitude. Specifically, the point estimates for initial STEM enrollment and degree attainment, taken at face value, imply effects of a one standard deviation increase (about 3.6 courses) in courses available per 100 students on postsecondary STEM outcomes of 0.10 to 0.15 percentage points. These equate to about 0.7% to 0.8% of the baseline rates of STEM enrollment and completion of 21% and 12%, respectively.
Moreover, even at their upper bounds, the implied effects are modest at best. The upper bound of the 95% confidence interval for the course-access coefficient in the STEM enrollment model is about 0.70 percentage points; in the STEM attainment model, it is 0.57 percentage points. These upper bounds correspond to just 3% and 5% of the sample means of these outcomes, respectively.
The models in Table 4 use all high school math and science courses to measure STEM exposure. We next use separate measures to explore the potential for effect heterogeneity of exposure to math and science courses and to math courses that differ by the level of content covered. Access to different types of courses, and in particular differential access to advanced courses across demographic and socioeconomic groups, has received significant attention in research (e.g., see Conger, Long, & Iatarola, 2009; Klopfenstein, 2004).
Table 5 shows results from models that permit effect heterogeneity between math and science courses, and between math courses by level. All results are from our full specification. There is no evidence that differential exposure to math or science courses separately in high school affects postsecondary STEM enrollment or attainment. Similarly, there are no differential effects of access to regular versus advanced math courses. The point estimates throughout Table 5 are small, fluctuate in sign, and none are close to statistically significant at conventional levels.
STEM Major and Degree Attainment Models, With Course-Type Heterogeneity
Source. Administrative data on Missouri public HS students who matriculate into a Missouri public 4-year university.
Note. Courses available only. Course availability is courses available per 100 students, standardized to have a mean of zero and a standard deviation of one. All models control for high school fixed effects, student race/ethnicity and gender, student ACT math and English scores, student high school class rank, enrollment in the high school, percent minority in the school, percent free/reduced-price lunch in the school, and high school graduation year (year fixed effects). Standard errors clustered by high school included in parentheses. STEM = science, technology, engineering, and mathematics; FE = fixed effects; HS = high school.
p < .05. **p < .01.
Sensitivity
Period Subgroups
The key identification threat in our models is the potential for endogenous changes to course offerings within high schools over time. Because our results are primarily null, the main concern is negative bias, which might come about if, for example, high schools where STEM training or interest is trending downward respond by offering more courses, and vice versa. This would induce a negative correlation between courses available within high schools over time and subsequent STEM outcomes, which, in turn, could generate null results from our specifications even if STEM access in high school positively affects postsecondary STEM outcomes, all else equal. We do not view this type of biasing scenario as likely. Instead, it seems more likely that our estimates, if anything, would be biased upward because changes to STEM course offerings within high schools over time are likely positively correlated with changes to the quality of STEM training and/or STEM interest within a high school. Nonetheless, the general biasing threat merits attention; if for no other reason than from a mechanical standpoint, over a 14-year span, many factors within a high school can change and we rely critically on the high school fixed effects for identification.
We test indirectly for the influence of potential bias from endogenous changes to course offerings over time by replicating our primary results using partitions of the full data set. We hypothesize that if bias from endogenous changes within high schools is present, model replications based on data that cover a shorter time span will be less biased because there is less time for major changes. We would view substantial differences in our estimates when we go from using the full data set, to using just a portion of the data set from a shorter time period, as a likely symptom of endogenous changes to course offerings within high schools over time.
Table 6 shows results from replications of our main model estimated on data sets that split the data over time in half (columns 2 and 3) and in thirds (columns 4–6). For ease of comparison, we re-produce our main estimates from Table 4 in column 1. The findings are generally consistent across the various time partitions of the full data set. The point estimates are small and statistically insignificant, with one exception (the coefficient in column 6 for the degree attainment model is statistically significant at the 10% level), and they nominally flip sign in one case (initial major model, column 5). Taken as a whole, we interpret the results in Table 6 as suggesting that endogenous changes to course offerings within high schools over time are unlikely to drive our null findings.
STEM Major and Degree Attainment Models, Various Time Periods
Source. Administrative data on Missouri public HS students who matriculate into a Missouri public 4-year university.
Note: Courses available only. Course availability is courses available per 100 students, standardized to have a mean of zero and a standard deviation of one. All models control for high school fixed effects, student race/ethnicity and gender, student ACT math and English scores, student high school class rank, enrollment in the high school, percent minority in the school, percent free/reduced-price lunch in the school, and high school graduation year (year fixed effects). Standard errors clustered by high school included in parentheses. STEM = science, technology, engineering, and mathematics; HS = high school; FE = fixed effects.
p < .05. **p < .01.
We also briefly mention a related test for this type of bias, in which we estimate models that include high school–specific linear time trends. This narrows the identifying variation further by isolating deviations from the trend for each high school over the time span of the data. Given that our results even without the high school–specific time trends are null, and that these models are more demanding from a statistical power perspective (i.e., our standard errors are larger), it is unsurprising that these models do not overturn our null findings (results omitted for brevity).
Alternative Measures of Course Access
We reestimate our models using two other measures of course availability. The first is analogous to our preferred courses-per-100-students measure, but is unadjusted for student enrollment at the high school. This allows for the possibility that absolute course access is important regardless of the size of the student body. The second measure is the above-described topical measure—such as our primary measure, it is adjusted into per-100-student units, but it does not double count repeat courses as expanding STEM access. Results using these alternative measures are shown in the online Supplemental Table S3. They are substantively similar to our primary findings in Table 4.
Another dimension of sensitivity we explore is with respect to the potential for access to advanced math courses late in the high school career to be particularly important. To do this, we construct measures of course access analogous to what we use above, but restricted to Grades 11 and 12 only. We focus exclusively on access to advanced math courses for this extension because students are likely to disproportionately take these courses in later grades, making exposure measures linked to students only in Grades 11 and 12 more plausibly congruent. Another way to frame this sensitivity test is that the measures of access restricted to Grades 11 and 12 allow us to test for the possibility that our earlier models understate the importance of access to advanced math courses due to mismeasurement—that is, because we partly measure access to these types of courses in Grade 10, when few students could plausibly take them. To push further on this, we additionally subdivide the group of courses we have identified as “advanced” into “college preparatory” and “college level” math courses. Examples of the former include geometry, precalculus, trigonometry, and calculus. Examples of the latter include IB mathematics, advanced placement (AP) statistics, AP calculus AB, and AP calculus BC. All these courses are grouped together as “advanced math” courses in our main models.
The results from this extension are reported in the online Supplemental Table S4. They are similar to our main findings in Table 5 regarding access to advanced math courses more broadly during high school. Specifically, the point estimates are small, statistically insignificant, and inconsistent in sign, thus aligning with our null results more generally.
Dual-Credit Courses
Our administrative data panel from DESE covers all courses offered in Missouri public high schools. Although these data are fairly comprehensive, there is a blind spot with respect to some dual-credit courses. Dual-credit courses are courses for which students can receive high school and college credits simultaneously. These courses can be given at high schools or postsecondary institutions. Courses offered at high schools and taught by high school faculty should be captured by the DESE core data used in our analysis, but courses offered at postsecondary institutions are not. 28 This poses a potential threat to identification because high schools could respond to dual-credit courses available at postsecondary institutions. A specific concern is that high schools may adjust their own course offerings in response to (unobserved) dual-credit offerings at a local postsecondary institution, in which case our estimates would be biased toward zero, calling into question the credibility of our null findings.
One factor that makes bias from this source less of a concern is that the “dual-credit footprint” in Missouri during the time span of our study was small. To explore this, we used a separate DESE data file on dual-credit courses from 1999 to 2008. 29 Over this period, dual-credit math and science enrollment of all types (i.e., whether offered at high schools and postsecondary institutions) accounted for just 1.1% and 0.7%, respectively, of total math and science course enrollment among Missouri high school students. It is also the case that “the large majority of dual-credit courses are taught by high school faculty” (Missouri DHE, 2011, p. 51), which means that most are captured in our data. To confirm this, we analyzed the same data file of dual-credit courses and found that 92% and 94% of students enrolled in math and science dual-credit courses, respectively, were enrolled in courses offered by K–12 school districts. Of these courses, approximately 85% and 92% can be found in the core course data (which we use in our primary analysis) matched to the school and year in which students were enrolled. Based on these figures, just a small fraction of total dual-credit enrollment in math and science is unobserved in our primary data. 30
In summary, the fraction of total high school math and science enrollment in dual-credit courses is small. When we further account for the fact that most students who take dual-credit courses take them in high schools, and most of these courses are matched to the high school and year in our data, the scope for bias in the small share of unobserved dual-credit courses in our analysis seems quite limited. 31
IV Extension
We now turn to the IV models described in section “Empirical Approach.” Under the more restrictive assumption that the only pathway by which increased course access in high school affects postsecondary STEM outcomes is by directly affecting students’ own course-taking behaviors, the IV estimates can be interpreted as causal effects of course-taking. Although the effect of course availability on students’ own course-taking is a plausible first-order pathway for effect, we again note that to the extent that the exclusion restriction is violated, we would expect the IV estimates to be biased upward due to other positive benefits associated with more STEM course availability in high school, such as effects on peers (and vice versa for reduced availability).
The first stage of the IV framework is useful for thinking about the mechanism underlying our null findings. If increased course-taking is the main pathway for effect of increased availability, the strength of this mapping—reflected in the first stage—is critical. Table 7 shows first-stage results for two versions of Equation 4, with results from the full version shown in column 2. High school course availability is a statistically significant predictor of individual student course-taking. However, it is not a strong instrument. In column 1, the F statistic is below the Stock and Yogo’s (2005) weak identification threshold value of 16 (10% maximal IV size). In our full model, in column 2, it is even smaller, well below the conventional threshold for a weak instrument.
Results From First-Stage Regressions of Course-Taking on Course Availability
Source. Administrative data on Missouri public HS students who matriculate into a Missouri public 4-year university.
Note. Course availability is courses available per 100 students. All models control for high school graduation year (year fixed effects). Student controls are race/ethnicity and gender, ACT math and English scores, and high school class rank. High school controls include location (urban, suburban, or rural; this factor drops out with the inclusion of HS fixed effects), enrollment, percent of the student body that identifies as a minority race/ethnicity, and percent of the student body that is free or reduced-price lunch eligible. Standard errors clustered by high school included in parentheses. HS = high school; FE = fixed effects; LM = Lagrange multiplier.
p < .05. **p < .01.
Substantively, the first-stage results indicate that for every one-unit increase in the average number of courses available per year per 100 students during high school, a student’s own cumulative course-taking increases by just 0.02 to 0.04 courses. To put this number in context, we can perform a rough back-of-the-envelope calculation of the “conversion rate” of courses available, as measured in our models, to total courses taken during high school. Assume the following: Each class has a capacity of 20 students (around the average for math and science classes in our data), students are distributed across classes at random, classes are filled to capacity, and expansion into an extra STEM course does not crowd out any other STEM course for individual students (the last two assumptions are essentially that there is excess demand for STEM courses). Under these assumptions, a one-unit increase in our measure of course availability per year during high school could increase the total number of STEM courses taken for an individual student by up to 0.60 courses. 32
Our estimates in Table 7 fall well short of this level and in fact, they imply expanded course access does very little to increase STEM course-taking. Put another way, our estimates suggest what is very close to a pure substitution with other STEM courses when STEM course offerings increase. Moreover, our sample conditions on 4-year public university enrollees, who are positively selected among high school students in Missouri (per Table 1, the average class rank in our sample is above the 70th percentile). If students in our positively selected sample are more interested in STEM coursework than the average high school student, the expected conversion rate would be higher in our sample than is implied by our simple back-of-the-envelope calculation.
Thus, although course-taking is technically responsive to course availability as indicated by the statistically significant estimates in Table 7, the level of responsiveness is modest and not consistent with the presence of widespread excess demand for math and science courses in high school. This result could reflect a lack of demand for more STEM coursework in high school unconditionally, for example, because of a general lack of student interest in STEM content or simply because students do not perceive a shortage in the availability of STEM courses. It may also be that the lack of a course-taking response is the result of other constraints on students during high school, such as to take courses in other fields for high school graduation and college admittance. Disentangling these mechanisms seems like a useful direction for future research, but regardless of the source, the weak first-stage estimates help to explain our null reduced-form results in Table 4.
The first-stage estimates also have implications for the interpretation of the reduced-form findings. Although our investigation was initially motivated by an interest in what is best described as an extensive margin intervention, the lack of a behavioral response of students on the extensive margin means that the primary treatment experienced by most students is on the intensive margin, in the form of smaller STEM classes. This is not to say that our analysis is not informative about the extensive margin, as the pass-through result in Table 7 is critical to understanding policies that aim to expand course access, but ex post, it is useful context that the way most students are affected by expanded course access is in the form of smaller STEM classes. Inadvertently, our reduced-form findings speak to the potential for policies aimed at reducing STEM class sizes in high school to affect postsecondary STEM outcomes.
In the online Supplemental Appendix, we probe our findings within the IV framework in several ways. Online Supplemental Tables S5 and S6 show results from first-stage regressions that use the alternative measures of course access as instruments (course availability unadjusted for enrollment and topic availability). The substantive finding from the first stage—that is, that the mapping from course access to course-taking—is upheld. 33 In the online Supplemental Table S7, we return to our preferred, enrollment-adjusted measure of course access, but divide the course access instruments by course type, as in Table 5. There is some evidence that expanded access to advanced math courses, in particular, results in more STEM course-taking in high school. However, the pass-through implied by the first-stage coefficients remains modest and the substantive finding of a weak first stage remains. 34 On the whole, the various first-stage results reported in Table 7 and the online Supplemental Appendix are consistent in showing weak pass-through of course access to course-taking in high school.
Finally, given that our instruments are weak, it is well-understood that we can glean little insight from the second-stage regressions. Nonetheless, for completeness, we show second-stage results from our main specification in the online Supplemental Table S8. The table shows that even under the strict IV assumptions, there is no clear evidence that additional course-taking in high school improves postsecondary STEM outcomes, although large effects (positive or negative) cannot be ruled out. Although the first-stage regressions are informative about our investigation of course-access effects, our study is ultimately not informative about the effects of high school course-taking.
Effect Heterogeneity
Next, we consider the possibility that the effects of course access vary by the racial/ethnic composition of the high school. This might be expected if, for example, high schools with higher percentages of minority students offer less access to STEM courses, in which case we might expect greater response elasticities to changes in course offerings at these schools. The descriptive statistics in Table 3 provide no prima facie indication of this, but some heterogeneity in course access—particularly in narrow pockets of the distribution such as among very high minority-share high schools—could be obscured in Table 3.
We focus on minority students who are underrepresented in STEM fields as a group (Black and Hispanic students) because of their importance to policy and due to sample size considerations in Missouri. We estimate separate models for three overlapping subsets of schools: those with underrepresented minority student shares above 25%, above 50%, and above 75%. The former group subsumes the latter groups, but not the reverse. The reason for the overlapping samples is that only a small fraction of Missouri high schools contain substantial minority student shares—for example, the 75th percentile high school in the state distribution has a minority share of just 18%. The structure of our investigation allows us to balance our interest in examining effect heterogeneity across high schools that differ as much as possible along this dimension against the loss of statistical power as the sample shrinks.
Table 8 shows results from our courses-taken and courses-available models akin to Table 4. For brevity, we only report findings from the fully specified models. As shown in the top panel of Table 8, like with the estimates from the full sample, we estimate a strong positive relationship between STEM courses taken in high school and initial enrollment in a STEM field. The magnitudes of the estimates are somewhat smaller in Table 8 than in Table 4, but lead to a similar conclusion. In contrast, the results from the degree attainment models in the last three columns, even when we use courses taken as the independent variable of interest, are much weaker than what we show for the full sample in Table 4 and not statistically significant.
STEM Major and Degree Attainment Models, by High School Racial/Ethnic Composition
Source. Administrative data on Missouri public HS students who matriculate into a Missouri public 4-year university.
Note. The high school underrepresented minority shares are calculated as the sample average enrollment shares of Black plus Hispanic students from NCES data, covering all students in all years of the data set. Course availability is courses available per 100 students, standardized to have a mean of zero and a standard deviation of one. All models control for high school fixed effects, student race/ethnicity and gender, student ACT math and English scores, student high school class rank, enrollment in the high school, percent minority in the school, percent free/reduced-price lunch in the school, and high school graduation year (year fixed effects). Standard errors clustered by high school included in parentheses. STEM = science, technology, engineering, and mathematics; HS = high school; FE = fixed effects; NCES = National Center for Educational Statistics.
p < .05. **p < .01.
High attrition rates from STEM fields have been well-documented, as have differential attrition rates by race/ethnicity (e.g., NSF, 2014). A potential explanation for the racial/ethnic attrition gaps suggested by previous research is that different groups are differentially prepared to succeed in STEM (e.g., Arcidiacono, Aucejo, & Spenner, 2012). Among students in high schools with large proportions of minority students, our results suggest that variation along at least this one dimension of preparation—high school STEM coursework—does not positively map to STEM success in college, even in models that embody endogeneity owing to students’ own course choices in high school.
Moving to the models of course access in the bottom panel of the table, where we have more causal purchase, there is no evidence that increased exposure to STEM courses in high school corresponds to improved STEM outcomes in college among students who attend high schools with a high proportion of minority students. If anything, the reverse is weakly suggested by the mostly negative point estimates, several of which are statistically significant or on the margin of being so. Inference is similar when using our other measures of course access and when we break out science and advanced/regular math courses (results available upon request).
Next, in Table 9, we examine effect heterogeneity by race/ethnicity and gender at the individual student level, within high schools. Following Table 8, for race/ethnicity heterogeneity, we focus on comparing White students with Black and Hispanic students. The models interact our primary measure of course availability with indicators for students’ genders and race/ethnicities. Male and White students are the omitted comparison groups, and thus effects for all other groups are relative to them. For brevity, we show results only for the fully specified models of course access.
STEM Major and Degree Attainment Models, With Race/Ethnicity Heterogeneity
Source. Administrative data on White, Black, and Hispanic Missouri public HS students who matriculate into a Missouri public 4-year university.
Note. Courses available only. Course availability is courses available per 100 students, standardized to have a mean of zero and a standard deviation of one. All models control for high school fixed effects, student race/ethnicity and gender, student ACT math and English scores, student high school class rank, enrollment in the high school, percent minority in the school, percent free/reduced-price lunch in the school, and high school graduation year (year fixed effects). Standard errors clustered by high school included in parentheses. STEM = science, technology, engineering, and mathematics; HS = high school; FE = fixed effects.
p < .05. **p < .01.
Column 1 shows results when the outcome is initial STEM enrollment. There is statistical evidence of effect heterogeneity by gender and race, but the magnitude is small to moderate. The estimate for women, statistically significant at the 10% level, implies that a one standard deviation increase in course access during high school has an effect on STEM enrollment that is 0.46 percentage points lower relative to White men. For the race/ethnicity comparison, the −1.14 percentage point effect for underrepresented minority students relative to White men is somewhat larger and corresponds to an effect size of about 5.5% of the sample mean for a one standard deviation increase in course access. When we turn to the model of degree attainment, the race/ethnicity and gender gaps moderate and become statistically insignificant.
For both women and underrepresented minorities, and in both models, the overall effects of increased course access, inclusive of the main coefficient, are small and statistically insignificant. Moreover, the differential effects relative to White men are best described as small to moderate. Still, the direction of the findings is not encouraging about the prospects for using high school STEM access as a policy lever to promote STEM diversity. The results suggest that expanded course access in high school could modestly widen postsecondary STEM enrollment gaps by race and gender. 35
Conclusion
We use administrative data from Missouri covering 14 cohorts of entering postsecondary students to examine the effects of access to STEM courses in high school on STEM outcomes in college. A lack of access to STEM courses in high schools has been postulated as a barrier to STEM entry and success in college (e.g., Deruy, 2016; President’s Council of Advisors on Science and Technology, 2010; Randazzo, 2017; White House, 2016). Moreover, from a policy perspective, expanding STEM course access is an appealing margin to consider in efforts to improve postsecondary STEM outcomes because policy changes would be feasible and create less risk of adverse unintended consequences relative to analogous course-mandate policies (Allensworth, Lee, Montgomery, & Nomi, 2009; DeCicca & Lillard, 2001; Jacob, Dynarski, Frank, & Schneider, 2017).). However, using multiple measures of STEM course access in high school, including measures that separate exposure to advanced coursework in math, we consistently show that changes in course access do not causally affect postsecondary STEM outcomes.
We also explore the potential for effect heterogeneity across high schools that differ by the share of underrepresented minority students, and within high schools by student race and gender. A motivation for the cross-school heterogeneity analysis is the concern that access to STEM coursework is more restricted in high-minority high schools, in which case, we might expect students to be more responsive to changes in course availability. However, we find no evidence of effect heterogeneity along this dimension. Our large data set allows for a well-powered analysis of effect heterogeneity by race and gender within high schools, and we find some statistically significant differences, but they are modest. Furthermore, they suggest that postsecondary STEM outcomes for female and underrepresented minority students are less responsive to changes in access to STEM courses in high school than White males. The implication is that broad, untargeted efforts to expand STEM access in high school are likely to modestly exacerbate current race- and gender-based imbalances in STEM fields.
Our study is informative about an important and oft-advocated policy for improving postsecondary STEM outcomes, but we note several limitations. First, we caution that our results may not extrapolate well to changes in STEM course access outside of the range of observed values in our data. As an extreme example, our findings should not be taken to imply that reducing STEM access in high school to zero would have no effect on postsecondary STEM outcomes. And, although our reliance on natural variation in “business as usual” course offerings within high schools over time for identification is appealing in some ways as discussed above, it also limits the range of research questions we can answer. For example, interventions to improve the quality of high school STEM education on the intensive margin may offer more promise. It is not clear what characteristics of intensive-margin interventions would drive change (again, our results imply class-size reductions alone will likely be ineffectual), but possibilities include the development of a deeper, more stable STEM curriculum, and the use of incentives along the lines of the AP incentive program studied by Jackson (2010, 2014). Regarding the former, variability in “stable” STEM curricula would occur mostly across high schools, making our estimation strategy ill-suited to speak to the potential effects. But evidence to date on more substantial STEM interventions, such as STEM high schools, is not particularly promising (e.g., Wiswall, Stiefel, Schwartz, & Boccardo, 2014). More broadly, changes on the intensive margin can be effective if the standard approach to STEM education in high school can be improved. Margins for improvement might include recruiting better teachers, changing student and teacher incentives, and improving STEM facilities and instructional materials. However, it is important to recognize that resource-backed efforts to improve STEM education will likely crowd out resources targeted toward other types of learning, given educational budget constraints. Noting these challenges, the lack of effects of simple expansions in course access that we document here suggests that for high school STEM policies to be effective at promoting postsecondary STEM interest and success, the norm of high school STEM instruction will need to change.
Supplemental Material
DS_10.3102_0162373719876923 – Supplemental material for High School Course Access and Postsecondary STEM Enrollment and Attainment
Supplemental material, DS_10.3102_0162373719876923 for High School Course Access and Postsecondary STEM Enrollment and Attainment by Rajeev Darolia, Cory Koedel, Joyce B. Main, J. Felix Ndashimye and Junpeng Yan in Educational Evaluation and Policy Analysis
Footnotes
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: We gratefully acknowledge research support from the National Science Foundation (awards 1532015/1745287 and 1531920) and CALDER, which is funded by a consortium of foundations.
1.
Also see guidance from the President’s Council of Advisors on Science and Technology (2010), which recommends expanding the availability of advanced science, technology, engineering, and mathematics (STEM) courses in high school. Two other recent examples are, among policy and advocacy groups, Randazzo (2017), and in the media, 
, which is motivated by a report from the U.S. Department of Education’s Office of Civil Rights.
2.
As a concrete example of a counterpoint to the “STEM crisis” narrative, there is clear evidence of an oversupply of workers in some STEM fields and at some levels of education, most notably in the market for individuals with advanced degrees in biological sciences (Institute of Medicine, 2014; Offord, 2017).
3.
Jackson (2010, ) studies a program designed to promote advanced placement (AP) course-taking (not STEM focused) by providing monetary incentives to teachers and students. The incentives are substantial: up to a US$10,000 salary bonus for teachers plus additional performance incentives, along with exam fee and incentive payments to students (from US$100 to US$500) who pass the AP tests. Jackson (2010, 2014) finds effects on students ranging from null to positive on a variety of short-term and long-term outcomes and is generally positive about the program’s efficacy. Although useful for understanding how, and how much, targeted and resourced interventions can affect student outcomes, the near-term applicability of the findings for efforts to meaningfully scale up STEM training is modest because most schools do not have the resources to implement these types of programs.
4.
Our analysis conditions on university enrollment, which means that our data are well suited to examine shifts in major choice and attainment, conditional on entry into the 4-year public university system, but ill-suited to examine effects on the extensive margin of college (i.e., attendance). Below, we test for and find no evidence to support the hypothesis that the availability of high school math and science courses affects the composition of our sample of public 4-year college enrollees (see section “Tests for Effects on College Enrollment”).
5.
As noted below, 17% of the variance in course access occurs within high schools over time.
6.
Because variation in course access is such a weak predictor of course-taking, our study is ultimately uninformative about policies that require additional course-taking explicitly. Evidence on the effects of mandatory course-taking is mixed. Studies suggest short-term academic benefits but evidence on longer term outcomes is less promising because such initiatives can induce dropout (e.g., Allensworth, Lee, Montgomery, & Nomi, 2009; Cortes, Goodman, & Nomi, 2015; DeCicca & Lillard, 2001; Jacob, Dynarski, Frank, & Schneider, 2017; a related literature examines high school exit exams and similarly finds negative effects on graduation: for example, Jacob, 2001; Jenkins, Kulick, & Warren, 2006; Papay, Murnane, & Willett, 2010). The negative effects documented in some studies of course mandates make policies that expand course access without mandatory course-taking appealing.
7.
Students’ class ranks and ACT scores are determined during the treatment window (high school). A concern is that including these variables could dull the estimated coefficients of course access and course-taking. In recognition of this concern, we have estimated our models that exclude these control variables and confirmed that the results we show below are robust (results available upon request). We prefer the models that include the full suite of control variables for students because they improve precision with no indication that they substantively influence the parameters of interest.
8.
9.
10.
Some students will graduate after the 6-year window, but we follow convention in the literature of using 6 years for our primary analysis. Results are qualitatively similar when using graduation rates as measured over 7 or 8 years (omitted for brevity).
11.
The state increased requirements to three math and science courses starting in 2010, after the time span of our data.
12.
Other STEM includes technical subfields of education, military technologies, social sciences, health professions, and management sciences.
14.
As an example of how a marginal course would affect our enrollment-adjusted course availability measure, consider a student who attends a school with 100 students and where 10 STEM courses are offered in each year during her 10th- to 12th-grade experience. We would calculate that this student has access to 10 available courses in high school each year, on average, yielding a courses available per year per 100 students of 10.0 (30/3). If one extra course is added in Grade 12, but the Grade 10 and Grade 11 offerings do not change, then the value of our measure would change to 10.33 (31/3). If course offerings at this 100-student high school shifted to a new “steady state curriculum” of 11 courses each year during Grades 10 to 12, the value of our measure would increase by one full unit, to 11.0.
15.
Specifically, we coded courses as high school level, college preparatory level, or college level based on administrative course numbers, course grade level (a standardized reporting of the year in school in which students typically take the class), sequence number (identifies content of courses that are taught at more than one level), and delivery system.
16.
A notable variable is high school enrollment, which we use as a covariate in our fully specified models and to adjust our preferred course-availability measures. Given that our course-availability measures cover courses offered in Grades 10 to 12, we use enrollment in Grades 10 to 12 for consistency.
17.
The larger proportion of female students in our college-going sample is consistent with the well-documented female advantage in college entry (e.g., Bailey & Dynarski, 2011).
18.
Although student transfers out of STEM are higher than transfers into STEM, the STEM enrollment and attainment shares end up being similar because initial STEM majors graduate at higher rates.
19.
Based on the simple average of courses taken by public high school graduates in 1998, 2000, 2005, and 2009. See the Digest of Education Statistics, 2016, table 225.10, published by the U.S. Department of Education.
20.
For example, in math, this effectively includes high school courses above pre-algebra. These data come from students’ postsecondary records and, therefore, include courses taken outside of the Missouri public school system when applicable.
21.
There are a small number of observations (about 0.2%) with zero recorded math and science courses; although odd, this is not impossible, and our results are insensitive to the exclusion of these observations from the analytic sample.
22.
Note that the descriptive statistics are reported using the student-level data, and thus student weighted.
23.
We decompose the variance in course availability per 100 students by regressing this variable on the vector of high school indicator variables. One minus the R2 from the regression gives the share of the variance that occurs within high schools.
24.
Average high school enrollment for White students is lower than that for Black, Hispanic, and Asian students.
25.
The average class rank of university entrants in our sample is in the 70th percentile; among STEM entrants, the average class rank is in the 77th percentile.
26.
The two most important compositional concerns are (a) changes in STEM course access in high school could induce some students to enroll in Missouri 4-year public universities who would not have enrolled otherwise and (b) changes in STEM course access could induce some students to switch from 4-year Missouri public universities to different universities.
27.
28.
A small number of students during the time span of our study also take dual-credit courses delivered through an interactive television (ITV) system, which typically connects them to a course on a college campus. From a data perspective, ITV courses are similar to courses taken physically on college campuses, in that the Department of Elementary and Secondary Education (DESE) core course data files, upon which our main analysis is based, will not include these courses.
29.
The first year that dual-credit courses were tracked by DESE is during the 1998–1999 school year. The 2008–2009 school is the final year of high school for the latest cohort in our analytic sample, but data on dual-credit courses in that year are missing (this is an idiosyncratic omission in the data files). Thus, we use the data period of 1999 to 2008 for our exploration of dual-credit courses (school years denoted by spring years). Also note that dual-credit enrollment has grown in recent years in Missouri and, as of 2018, accounted for roughly 3.0% and 1.8% of math and science high school course enrollment, respectively.
30.
The match rates of 85% and 92% are high, but one could argue they should be even higher because dual-credit courses offered in high schools should be taught by high school instructors. We can only speculate as to why the match rates are not higher, but we suspect two reasons. First, districts may rely on outside personnel in some limited cases. Second, and more important, given that Missouri has many rural schools with limited course offerings, some students may take dual-credit courses in other schools or districts, in which case there would not be a “home school” match for the dual-credit course in the core data. Regardless of the cause, both of these are examples of data issues that result in an imperfect characterization of course availability at the school-by-year level in our core analysis. But together, they still result in just a small fraction of high school courses that are unobserved.
31.
Finally, we also note that dual-credit course availability and enrollment steadily increased during the time span of our data panel, with enrollment in math and science starting at about 0.6% and 0.4%, respectively, when DESE first began tracking D.C. courses in 1999, and rising to 1.4% and 0.8% by 2008. The pattern of results over time in gives no indication that our results change during later periods with more dual enrollment, which is further evidence that our null findings are not the result of bias due to the availability of unobserved dual-credit courses.
32.
To elaborate briefly, at the upper bound with a course capacity of 20 students, if 20/100 students take each offered course and each course is accessible and not redundant, the simple expected increase in total courses taken during high school for a student who is exposed to one more course per year on average for 3 years (which is what is indicated by a 1.0 unit increase in our measure of course availability) is 0.60. A simple calculation of the lower bound is more difficult because pass-through can be affected by additional constraints, such as whether marginal courses fit into students’ course sequences, students are otherwise eligible for courses, and whether new courses are on new topics. That said, if we use our “topic availability” measure of course access, it is fairly easy to arrive at a lower bound of 0.20, and the online Supplemental Appendix shows that our results are similar (and even weaker) using that measure in the first stage (see the ).
33.
An explanation for the weak predictive power of our topical-availability instrument is that math and science courses on different topics may be viewed as substitutes by students attempting to satisfy various high school graduation and college requirements. In such a scenario, measures that privilege nonrepeat courses at the expense of fully measuring capacity will be less predictive of students’ course-taking behaviors.
34.
Although the first stage based on our full sample of college attendees is weak, the evidence in the suggests an area for future research. Namely, it may be that among a more targeted sample of high-performing students, and/or students with clear math and science aspirations, access to more advanced math courses may be particularly valuable. This possibility is not ruled out by the generally weak effect we estimate for our broad sample of college attendees.
35.
This is consistent with findings from Conger, Long, and Iatarola (2009).
Authors
References
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