«Clive Belfield Queens College, City University of New York Vivian Yuen Ting Liu Community College Research Center Teachers College, Columbia ...»
The Labor Market Returns to Math Courses in
A CAPSEE Working Paper
Queens College, City University of New York
Vivian Yuen Ting Liu
Community College Research Center
Teachers College, Columbia University
The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education,
through Grant R305C110011 to Teachers College, Columbia University. The opinions expressed are those of the
authors and do not represent views of the Institute or the U.S. Department of Education. We appreciate comments and help from Shanna Smith Jaggars and Di Xu. We also appreciate help from personnel within the North Carolina Community College System.
Abstract This paper examines the returns to math courses relative to courses in other subjects for students in community college. Using matched college transcript and earnings data on over 80,000 students entering community college during the 2000s, we find that college-level math coursework has an indirect positive effect on award completion that is stronger than that of coursework in other subjects. In terms of direct effects, we find mixed evidence on the direct effect of enhanced math skills on earnings over other college-level skills. Overall, the combined direct and indirect effect appears to be adverse: compared with other courses or college pathways, more math coursework in community college is modestly associated with relatively lower earnings in later adulthood. However, this association is sensitive to modeling, and we do find heterogeneous results by gender, race/ethnicity, and initial college ability, as well as by math field and level.
Table of Contents
1. Introduction 1
2. The Economic Value of Math Skills 2 Math Skills in High School 2 Math Skills in College 4
3. Model for Estimating Returns to Math Courses 6
4. Dataset 8
5. Results 9 Math in Community College 9 College Math and Award Receipt 11 College Math and Earnings 11 College Math and Earnings: Instrumental Variables Estimates 17
6. Conclusion 19 References 21 Appendix 25
1. Introduction A significant body of evidence has found that math skills have especially high and durable economic value both at the individual and aggregate levels. The academic value of math skills is evident from early childhood and persists through the high school and college years;
these gains then transfer into the labor market such that earnings are higher for persons with more math preparation (Duncan et al., 2007; Jamison, Jamison, & Hanushek, 2007; Rose & Betts, 2004). Directly, these math skills may influence earnings insofar as they are relatively more valuable than other forms of human capital in the labor market. For example, the National Academy of Sciences, the National Academy of Engineering, and Institute of Medicine (2007) catalogued an inventory of technological innovations (in, e.g., transport, communications, energy power, and information processing) that relied on advanced math. Indirectly, math skills may raise earnings through their effects on credential attainment, such as completion of high school or college (Aughinbaugh, 2012). Given these benefits, there is continued policy pressure on practitioners to improve the math skills of students.
However, almost all the research to date has looked at high school math. The evidence on college math is very sparse. Yet, in concert with policies to improve high school math, there is now an intensive policy movement toward improving college-level math skills. Several strategies are being developed, although so far they have not been very successful (Hodara, 2013). One strategy is early assessment—helping high school students avoid math remediation in college by providing information on their math readiness prior to enrollment. In itself this information seems to be an insufficient incentive for students to enhance their math skills in high school;
furthermore, collaboration between schools and colleges is often not very deep. A related strategy is to provide pre-enrollment supports for students, such as summer bridge programs or boot camps. Thus far, the limited available evidence shows these supports have only weak effects. A third strategy is the reform of developmental (remedial) math, including the shortening of the remedial sequence or better aligning remedial courses with college-level requirements.
These reform strategies vary substantially but overall the evidence shows “trivial to small” effects. A final strategy is to improve college math instruction, often through the use of innovative technology. Although promising, the increased use of computer-mediated math instruction has had mixed results so far. 1 For college-level math, these reform strategies have two presumptions. One is that the way to enhance math skills is to improve the quality of existing math instruction. This is problematic because most students take hardly any college-level math. Looking at community college students across the United States, only 40 percent complete an introductory math course, On summer bridge programs, a recent randomized controlled trial found no difference in college-level math pass rates after two years between those who participated in the program and those who did not (Barnett, Bork, Mayer, Pretlow, Wathington, & Weiss, 2012). On compressing courses, modularization, and learning communities, Hodara (2013, Appendix B) reported weak effects. On improving math instruction, student collaboration and pedagogic use of multiple representations have been shown to have some positive effects on math achievement (Chappell, 2006).
and more than half of all students leave college without any college-level math (US DOE, 2012).
Thus, many students would be unaffected by these reforms. But the more fundamental presumption is that enhancing college-level math is economically valuable. For a broad swath of students, however, there is very little evidence as to whether this presumption is valid and thus whether it is worth redesigning the math coursework students take in college.
In this paper, we estimate the labor market returns to college math for community college students. We begin by reviewing evidence on the importance of math skills: we juxtapose the substantial evidence on high school math skills with the dearth of evidence on college math skills. We then specify our model for estimating the labor market effects of college math skills.
Our estimation sample is two full cohorts of community college students in North Carolina for whom we have full transcript data and labor market data up to nine years after first enrollment.
Few community college students intensively study math subjects, so our analysis pertains to general math skills (not skills associated with math majors). We estimate earnings gains for incremental math skills for the full cohort and for subgroups of students. Finally, we conclude with a discussion of the implications of policies that seek to improve math skills in community college students.
2. The Economic Value of Math Skills
Math Skills in High School For high school students, a substantial body of research highlights the importance of math course-taking on educational attainment. There is a clear association with high school graduation. Using data from the Educational Longitudinal Study of 2002 (ELS:2002), Bozick and Lauff (2007) reported that 52 percent (61 percent) of students who take no (basic) math graduate, whereas almost every student who takes calculus graduates. Using hierarchical linear modeling with data from the National Education Longitudinal Study of 1988 (NELS:88), Lee and Burkam (2003) estimated that a one-standard-deviation increase in 10th-grade math GPA reduces the odds of dropping out of high school by one-third (see also Zvoch, 2006). These gains in high school affect college attendance: using a fixed effects specification, Aughinbaugh (2012) estimated that students who take advanced math in high school are 17 percentage points more likely to enroll in college; and, using a regression discontinuity design, Cortes, Goodman, and Nomi (2013) found sizeable increases in college enrollment for students assigned to “doubledose” algebra. Also, more high school math is associated with lower math remediation in college (Long, Iatarola, & Conger, 2009). Finally, advanced math in high school is strongly associated with completion of college, with an impact even greater than that of high school GPA and socioeconomic status (Adelman, 1999). Although consistently large, these attainment effects do vary by gender and race.
Even as this evidence is not causal, it consistently emphasizes the benefits of more advanced math skills. Thus, these skills are likely to improve labor market outcomes, either directly through increased productivity and or indirectly through their association with further human capital attainment.
Indeed, most evidence thus far has found that math skills—measured during high school—have a powerful effect on earnings (see Altonji, Blom, & Meghir, 2012, Table 2). Again this evidence is based on correlational studies, which typically estimate the overall—direct and indirect—effects of math. In reviewing four studies, Hanushek (2006) estimated an earnings premium from a one-standard-deviation increase in math test scores of 12 percent. Goodman (2012), exploiting the differential timing of state-level increases in high school graduation requirements in the 1980s, found that post-reform students took more math courses and earned significantly more than those who had faced weaker pre-reform math requirements. Using the National Longitudinal Survey of Youth of 1979 (NLSY79), Blackburn (2004) found the math subtests of the Armed Forces Qualification Test (AFQT) administered to teenagers to have the strongest correlation with later earnings: a one-standard-deviation increase in the numerical operations score increased wages by 2.8 percent. In contrast, using NELS:88, Rose (2006) found weak effects, in part because of the heterogeneity of test scores on graduation probabilities. Also, using instrumental variables specifications on NELS:88 and ELS:2002 data, Gaertner, DesJardins, and McClarty (2014) found no clear effect of high school Algebra II on earnings a few years after high school.
However, using High School and Beyond data with a 10-year follow-up, Rose and Betts (2004) estimated the effects of each math course on earnings separately: progressively stronger impacts were evident for more advanced math, with calculus credits having a very strong influence on earnings. Staying in school for an extra year, but with a course load with no math, added only 2 percent to earnings; if the extra year included calculus in the course load, earnings were 9 percent higher (Rose & Betts, 2004, Table 4). 2 Finally, Koedel and Tyhurst (2012) used a resume-based experiment to identify significant hiring advantages for applicants with greater math skills.
The evidence from high school also shows that enhancing math skills may be differentially effective on earnings. For racial/ethnic minorities, Goodman (2012) showed that higher math requirements for Black males can explain almost the entire wage premium from a year of additional schooling. For gender, Rose (2006) found the overall null effect did not hold for female students, who obtained a 9 percent advantage when their math test scores were one standard deviation higher (and reported higher labor market participation rates). Finally, looking across the ability distribution, Rose (2006, Table 5) reported significantly higher earnings as math scores of those in the bottom quartile of ability improved, with weaker gains for those with Similar results are found internationally (on evidence from a pilot program in Denmark, see Joensen & Nielsen, 2009; for England, see Dolton & Vignoles, 2002).
greater math skills. Hence, improving math skills in school may help close earnings gaps across subgroups.
Math Skills in College By contrast, there has been very little research on the value of college math in terms of either its direct skills effect or its indirect attainment effect. Studies have looked at remedial math and college success, typically concluding that it does not help students succeed in college (Bailey, Jeong, & Cho, 2010). Also, using a regression discontinuity design for remedial math course-taking, Martorell and McFarlin (2011) found no effect on earnings. Hodara and Xu (2014) also found a null effect of remedial math on earnings. But this failure may be because of either adverse selection into remediation, or incorrect assignment to remediation, or the delay to enrollment in college-level courses (Scott-Clayton, Crosta, & Belfield, 2014). Using NELS:88, Adelman (2006) did find some—but not consistent—evidence that college-level math courses are important for college completion; however, this descriptive study looked only at bachelor’s degree receipt.
At the four-year college level, there is evidence that majoring in math yields high labor market returns. Several studies have focused on the returns to STEM majors. Olitsky (2012) found high returns (of 5–28 percent) for students who majored in STEM compared with other subjects using propensity score matching (see also Melguizo & Wolniak, 2012). Thomas and Zhang (2005) found college math credits—bundled with engineering credits—to have a significant impact on earnings relative to other subjects taken by college graduates. Across postsecondary education including two-year colleges, most evidence on the association between college math and earnings comes from studies examining the returns to broadly defined disciplines such as social sciences or business (Hamermesh & Donald, 2008). Generally, these studies find higher returns for more quantitative disciplines (for a review of community college benefits, see Belfield & Bailey, 2011). From community college transcripts of displaced workers, Jacobson, LaLonde, and Sullivan (2005) calculated that a year of “more technically oriented vocational and academic math and science courses” raised earnings by 14 percent (29 percent) for male students (female students). In contrast, less technically oriented courses yielded no payoff. However, these studies identified the returns to a math major or to subjects with substantial math content.