College course scarcity and time to degree

Economics of Education Review 41 (2014) 24–39

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Economics of Education Review journal homepage: www.elsevier.com/locate/econedurev

College course scarcity and time to degree§ Michal Kurlaender a,*, Jacob Jackson a, Jessica S. Howell b, Eric Grodsky c a

University of California, Davis, United States The College Board, United States c University of Wisconsin, Madison, United States b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 28 April 2011 Received in revised form 21 March 2014 Accepted 30 March 2014 Available online 8 April 2014

College students are taking longer to earn baccalaureate degrees now than ever before, but little is known about institutional factors that may contribute to this trend. In this paper we investigate an important institutional constraint—course scarcity—that we hypothesize may be associated with increased time to degree. We employ a unique administrative dataset from a large, moderately selective, public institution and use an instrumental variables approach, identifying off the random registration times assigned to students. Results suggest that course scarcity does not delay students’ graduation. We explore alternative explanations for our findings and discuss a variety of other factors correlated with time to baccalaureate completion. ß 2014 Elsevier Ltd. All rights reserved.

JEL classification: I21 I23 Keywords: Higher education Time to degree Instrumental variables

1. Introduction Today, more students are enrolling in college than ever before, but increased access to postsecondary education has been met with stagnant completion rates (Turner, 2004) and increasing time to degree completion (Bound, Lovenheim, & Turner, 2012). Between 1972 and 1992, the mean time to a baccalaureate degree shifted from 4.69 years to 4.97 years. Outside of the top 50 public colleges or universities, average time to degree shifted from 4.71 years to 5.08 years (Bound, Lovenheim, & Turner, 2010a). Among the 2001 cohort of baccalaureate degree-seeking students, 36 percent

§ This project was supported by a grant from the Institute of Education Sciences of the U.S. Department of Education (#R305B070377). We thank the current and former Registrars at the University of California at Davis, Elias Lopez and Frank Wada for facilitating access to the data and for their helpful feedback on all aspects of this work. We also thank Chris Redder for his assistance with the data. Opinions reflect those of the authors. * Corresponding author. E-mail address: [email protected] (M. Kurlaender).

http://dx.doi.org/10.1016/j.econedurev.2014.03.008 0272-7757/ß 2014 Elsevier Ltd. All rights reserved.

graduated in four years, 16 percent took between four and five years, and 5 percent took between five and six years, the rest either took longer than six years or failed to complete (Wei & Horn, 2009). These statistics suggest that, among students who do obtain baccalaureate degrees within six years of entering college, at least 37 percent take longer than four years to do so. Bound et al. (2010b, 2012) suggest that the large aggregate shifts in time to degree occurred mostly among students beginning college at less selective public institutions, such as community colleges. Extended time to degree has a range of potential impacts, from increasing the cost of education for the student to suppressing the supply of college-educated workers in the economy. By extending their time in college, students pay tuition and fees for extra semesters, increasing the overall cost of their diploma. If a student uses loans to pay for college they must borrow more to pay for the extra semesters, thereby accruing more interest on earlier student loans. Moreover, if students extend time to degree, they may also be increasing the opportunity cost of the college investment, as forgone earnings increase.

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Longer time to degree may also have important impacts on the institution and the state in which the student attends school. From the institution’s perspective, a longer time to degree causes an unplanned increase in the number of continuing students, straining a university’s already increasingly scarce resources. Scarce resources may keep a university from admitting new students or distributing fewer resources per enrolled student (e.g. larger class sizes, fewer course offerings, and less academic or non-academic programs). Although continuing students pay tuition, about half of the cost of college for a student is subsidized by a combination of state and federal government support (Kane, Orzag, & Gunter, 2003). Similarly, some low-interest federal loans and grants, such as federal Pell grants, often support students through up to nine years of undergraduate work. Thus, longer time to degree may create additional burdens on state and federal grant and loan programs for postsecondary schooling. Ultimately, a longer time to degree may negatively impact the economy. Long delays in college completion affect the stock of college-educated workers that the U.S. increasingly demands (see Dynarski, 2005 for discussion). Students who fail to complete college never enter the supply of college-educated workers; however, if students are taking longer to graduate, the problem is slightly different. Although these students eventually enter the workforce with college degrees, their extended time to degree may slow the growth of the pool of collegeeducated workers (Scott-Clayton, 2012). Recent work on students’ collegiate outcomes suggests that changing student characteristics accounts for little of the upward trend in time to degree, but that the type of college attended and reductions in per-student resources available to colleges explain much of the time to degree trend (Bound et al., 2010a, 2012). In this paper we examine one possible mechanism for scarce resources impacting time to degree: students’ ability or inability to enroll in desired and required courses. If students are unable to enroll in a necessary or desired course, they may choose to enroll in fewer credits per term, change majors, take unnecessary courses, or engage in other behaviors that could increase their time to degree. We utilize a unique institutional data set and student registration audit data to examine whether constraints on student course choice lead students to take longer to earn a degree. 1.1. What do we know about extended time to degree? Most universities and degree programs require students to complete a minimum number of units in order to graduate. Students who have extended time to degree may be accumulating credits at a slower pace, which keeps them from finishing on time (Bound et al., 2010b; Bound & Turner, 2007). This could be a result of taking the minimum number of allowable credits each term as a full-time student or enrolling as a part-time student.1 Some students may not

1 Students are typically required to enroll in 12 units to be considered a full-time student for financial aid purposes, but that course load will not result in the completion of a degree in four years.

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attend college continuously, stopping out for one or multiple semesters without dropping out of school, which can lead to slower credit accumulation over time (Bound et al., 2010b; DesJardins, Ahlburg, & McCall, 2002; Horn & Carroll, 1998). However, it is also possible that students may be accumulating more credits than necessary to graduate. Although such accumulation may lead to an increase in human capital—in the form of more knowledge about a particular field, a double major or additional elective coursework—longer time to degree has not been met with rewards in the labor market, though such research is hampered by ubiquitous problems of self-selection. Researchers have explored a variety of student characteristics and behaviors associated with graduation and time to degree (DesJardins, Ahlburg, & McCall, 2006). Women are more likely than men to complete a degree in four years, and black and Latino students are more likely than white students to take longer than four years to complete a baccalaureate degree (Bradburn, 2003). Students requiring remedial coursework take longer to complete degrees than students who were not required to enroll in remediation (Adelman, 2006; Bettinger, Boatman, & Long, 2013). The means by which a student finances college may also impact his or her time to degree (Ehrenberg & Mavros, 1995; Glocker, 2011; Siegfried & Stock, 2001, 2006; Singell, 2004). Having to work while in school may impact a student’s time to degree (Bound et al., 2010a; Lamm, 1999; Volkwein & Lorang, 1996). And, students receiving grants are less likely to graduate on time than those using loans, controlling for other student characteristics. Though institutional factors may impact the length of time students take to complete their baccalaureate degrees, there is little research on the topic. Some sociological research suggests that student interaction with faculty, student peers and sense of community, active engagement with the institution, and mentoring all contribute to higher rates of persistence (Astin, 1993; Tinto, 1993), but not much has been written about time to degree. Although these studies provide sensible theories about college success, many of these studies fail to adequately control for observable and unobservable differences between students who select different kinds of colleges or collegiate experiences (Astin, 1993; Braxton & Hirschy, 2005; Tinto, 1993), and thus risk conflating the contributions of student characteristics to rates of postsecondary persistence with those of institutional practices and policies. Some studies have used differences between colleges to examine the impact of college characteristics on graduation outcomes. Colleges vary widely in the share of entering freshmen they graduate within four, five or six years. While the average four-year completion rate at four-year degreegranting institutions is a modest 34.5 percent, many schools graduate fewer than 15 percent of their students in four years while others graduate as many as 85 percent (Knapp, Kelly-Reid, Whitmore, & Miller, 2007).2 Reports by the American Association of State Colleges and Universities (2005) and The Education Trust (Carey, 2005; Hess,

2 The average six-year graduation rate at four-year degree-granting institutions rises to 56.4 percent (Knapp, Kelly-Reid, & Ginder, 2011).

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Schneider, Carey, & Kelly, 2009) speculate about why some public four-year colleges and universities are more successful than others at retaining students. Although both of these reports suggest that campus leadership on issues of retention may influence graduation outcomes, even when holding constant the typical set of institutional characteristics (e.g., size, sector, prestige, and average SAT/ACT scores), they do not provide direct evidence of how specific institutional policies affect college completion or time to degree. From more casual studies, we know that institutional quality makes a difference on student outcomes. Reviewing graduation rates of students who entered 27 elite colleges in 1989, Small and Winship (2007) find that college selectivity accounts for an appreciable share of the institutional variation in college graduation while other institutional characteristics, such as institutional endowment, contribute little to the variation in rates of degree attainment. Work focusing specifically on community colleges, has found less consistent evidence on the role of institutional quality measures on students’ outcome (Calcagno et al., 2008; Sandy, Gonzalez, & Hilmer, 2006; Stange, 2009). Most recently, Cohodes and Goodman (2012) exploit a unique scholarship in Massachusetts, and find that choosing a lower quality college significantly lowers on-time completion rates. Another set of studies by Bound et al. (2010a, 2010b, 2012) and Bound and Turner (2007) utilizes shifts in cohorts (based on a variety of characteristics) over decades in an attempt to explain what may have impacted time to degree for students. They find that increased time to degree is largest among students attending less selective public universities and community colleges (Bound et al., 2012). Their analyses suggest that decreases in institutional resources and cohort crowding, rather than changing student characteristics, accounts for the changes in time to degree. Specifically, a one percent increase in the number of eighteen year olds in a state is associated with a .71 year increase in the average time students in that state take to complete a baccalaureate degree (Bound et al., 2010a). Because students at public universities only pay a fraction of their total cost of education, an increase in college students results in fewer resources per student, given a constant level of support from the state. The authors suggest that reduced resources per student could impact time to degree through course scarcity. If students are unable to enroll in necessary courses, they may not take the full load of courses necessary to graduate on time. Moreover, they find that one specific sign of lower resources per student—lower faculty-student ratios—is associated with extended time to degree. Fewer numbers of faculty per student may also suggest less available courses per student, larger class sizes, and less student support. Finally, employing institutional level data from the Delta Cost Project, Webber and Ehrenberg (2010) explore institutional expenditures directly and find that student service expenditures, in particular, influence graduation and persistence rates, with effects largest among institutions with lower persistence and graduation rates. Institutions are increasingly aware of students’ lengthy path to a BA, and course scarcity is often identified among policymakers and consumers of higher education (stu-

dents and their parents) as a culprit for the increase in time to degree. Students may experience course scarcity when they are unable to enroll in their desired courses. Although course scarcity has received considerable attention in the popular press with articles such as ‘‘higher learning slows to a crawl,’’ (Los Angeles Times, October 4, 2012) little research has been done to investigate the impact of course scarcity on students’ graduation outcomes, specifically time to degree. In this study, we use data from the University of California, Davis (UCD) to search for a causal link between the likelihood of being denied courses and longer graduation times. Although nearly 85 percent of first-time freshmen eventually graduate from UCD, in a typical cohort, only 40 percent graduate within the traditional four-year span. In 2004, UCD formed a task force to identify factors contributing to a longer than desirable time to degree at the university, when compared to other UC campuses. The task force surveyed students and found that over 30 percent of students claimed that the inability to register for necessary or desired courses was one reason it may take them longer than four years to graduate. While 50 percent of students say they have been denied access to a class required for their major, 66 percent of students who are not on track to graduate within four years claim they have been denied access to a required class. Although student reports of course scarcity seem to suggest an impact on time to degree, there is no established causal link between the two. We use course registration records of student attempts to register for courses to determine a link between course scarcity and ontime graduation. In addition, we use the random variation in assigned registration time as an instrument to better identify the causal impact of course scarcity on time to degree. Our results show that course scarcity has a very small relationship with on-time graduation. When we investigate the causal relationship using an instrumental variables approach we find no link between course scarcity and on-time graduation. We explore several possible reasons for the counterintuitive result. 2. Research design 2.1. Data We employ data from the University of California, Davis (UCD), a large, land-grant university in the University of California system that serves about 22,735 undergraduates. As part of the University of California (UC) System, UCD affords entry to only the top 12.5 percent of the state’s graduating high school class,3 and boasts an average

3 The 1960 Master Plan outlines California’s higher education structure and defines the specific role of the University of California campuses, the California State University system, and the community colleges in the state. The plan articulates the University of California (UC) as the premiere research center offering graduate training through the PhD and providing undergraduate education for the top 12.5 percent of the state’s graduating high school class; the California State University (CSU) system is to provide graduate education through the masters degree, largely in ‘‘applied’’ fields, such as education and nursing, and the community college system as a place for open enrollment in sub-baccalaureate education and career technical training.

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39

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Table 1 On-time graduation rates by cohort. 4YGRAD

Fall 2002

Total (N)

3413

55.7 percent

Fall 2003

Fall 2004

59.9 percent 3362

59.0 percent 3005

Total 58.1 percent 9780

Notes: Analytic sample excludes students who had special registration priority (athletes, disabled students, etc.) and students who exit the university before spring of their fourth year.

combined SAT score of 1180.4 It has the third highest enrollment in the UC System (behind UCLA and UC Berkeley). The campus ranks fifth among the eight UC campuses in its four-year completion rate (44 percent). However, only one UC campus has a longer average time to degree length than the Davis campus. We examine longitudinal data from cohorts of entering first-time freshmen who started their postsecondary careers in fall of 2002, 2003 or 2004. The university provided student transcript and application data, including a variety of student characteristics (gender, race/ethnicity, parental education, parental income, and high school GPA). Importantly, we also observe term-by-term logs of student registration activity, including any attempts to enroll for a course. Finally, we observe term by term enrollment, including credits attempted and earned, major, academic performance (GPA), and the timing of degree completion. To arrive at our analytic sample, we first exclude any transfer students from our analysis, as well as the small number of students who drop out of UC Davis and do not return before the spring of their fourth year (less than 10 percent of all freshman).5 We also exclude students who received special priority registration at any point in their time at UC Davis, such as students with disabilities and athletes, which represents 2388 total students or 17.4 percent of all first-time freshmen in our sample. The pooled data from the three cohorts yields 11,337 first-time freshmen in our analytic sample. 2.2. Measures 2.2.1. Outcomes We are most interested in how course scarcity at the university impacts the time it takes for a student to obtain a degree. Among all students who enter UC Davis as freshmen, over 80 percent graduate from UC Davis, however, about 41 percent of all students who graduate do so after four years. This makes this large comprehensive moderately selective university an ideal setting to explore time to degree, and not such a great setting to explore persistence and BA completion; thus our primary outcome of interest is degree completion in four years. We define four-year completion first, as a dichotomous variable, 4YGRAD: baccalaureate diploma receipt within four years

4 Our calculations are based on the middle 50 percent of SAT scores as reported by the College Board. 5 We exclude students who exit the University because the focus of the paper is on time to degree. This is an extremely small number at UC Davis, as graduation rates are nearly 85 percent. Nevertheless, it does limit the generalizability of our sample some; a comparison of descriptive statistics between samples is presented in Table 2.

plus the summer following the 4th year (1 = yes, 0 = enrolled longer than four years).6 Table 1 details the on-time graduation rates for our sample. We note that overall about 58 percent of all students who persist until at least their fourth year graduate in four years. We also note that the percent of students graduating on time is on the rise at UC Davis (possibly in response to other institutional efforts beyond the scope of our investigation). We utilize a secondary outcome—time to degree—to check how robust our findings are to other specifications of on-time graduation. We define time to degree (TTD) as the number of terms between when a student enrolls as a firsttime freshman and when the student graduates. UC Davis uses the quarter system, in which a full time student attends fall quarter, winter and spring quarter, and then has the option of attending a summer quarter. Fig. 1 shows the distribution of time to degree by non-summer terms. The biggest jump in the distribution occurs at 12 terms, which is the traditional graduation time of spring in the fourth year.7 The second largest set of graduations occur throughout the fifth year (terms 13, 14 and 15), and then the sixth year shows fewer graduations (terms 16, 17, and 18). Some students do graduate before spring in their senior year, but those early graduations make up less than 10 percent of all graduates. 2.2.2. Key question predictor Although course scarcity can be measured at the campus level (i.e., the percent of courses that are full), we are more interested in course scarcity at the individual level and its potential influence on individuals’ on-time graduation. Our focus is on understanding how constraints on students’ ability to register for the courses they want or need impact their ability to graduate on time (defined as graduating within four years). We explore such constraints within UC Davis’s existing registration system, a system not unlike many large public four-year institutions. Students are grouped in priority groups based on accumulated credit bands; upper classmen get earlier registration times, however, within these credit bands registration times are randomly distributed (a feature we return to later in the paper). Students at UC Davis use an online system to register for classes. When students register for a course that is full they receive a message informing them that the course was full. We proxy for course scarcity with a measure of students’ individual level

6 Not all of these students graduate within our data window, but all are enrolled at some point at or beyond the spring of their fourth year. 7 We exclude the optional summer quarters from the analysis, so three terms represents a year at UC Davis.

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39

30 0

10

20

Percent

40

50

28

6

7

8

9

10 11

12

13 14 Term

15

16 17

18

19

20 21

8

Fig. 1. Distribution of time to degree. Notes: Sample excludes students who had special registration priority (athletes, disabled students, etc.), students who exited from the university before spring of their fourth year, and students that did not graduate from the university in our data window.

7.6

5

4.9

3.9

4

Average Shutouts

6

6.2

3 2.7

2.7

2

2

2

3

4

5

6

7 Term

8

9

10

1.8

1.9

11

12

Fig. 2. Average number of shutouts by term. Notes: Y-Axis represents the average number of shutouts for all cohorts in that term. Students with the top one percent of cumulative shutouts across all terms are omitted.

course shutout behavior. Our key predictor variable, SHUTOUTS, measures the average number of course shutouts a person experiences over the first four years at the University. We designate a shutout event as being shut out of a unique course section.8

8 For example, if a student tries to register for two different sections of biology 100, she will have two shutouts. However, if a student tried to register for the same section twice, she will have only one shutout.

Most students experience multiple shutouts while at UC Davis; the number of shutouts a student experiences varies from zero to well over 100. Given that the registration process privileges credit accumulation (i.e. upperclassmen get to enroll before freshmen), students are likely to experience more shutouts in their early years (Fig. 2). Fig. 3 illustrates the distribution of our key question variable SHUTOUTS, defined as the average number of shutouts experienced over students’ first four years at the University; the average is 3.9 and the standard deviation is

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39

0

2

4

Percent

6

8

10

29

0

2

4

6 8 10 12 14 Average number of shutouts per term

16

18

20

Fig. 3. Distribution of average number of shutouts per term. Notes: Histogram represents the average number of shutouts per term across a student’s first four years. Students with the top one percent of shutouts are omitted.

3.1. Some students have an enormous amount of average shutouts, over 40 per term. To deal with the potential skew and high leverage of these students, we omit the students above the 99th percentile on average number of shutotuts.9 Shutouts are not randomly distributed across students. First, students are more likely to be shut out of a course the later they register and, correspondingly, the fewer credits they have accumulated. We control for these dimensions, along with a host of others that may be associated with both shutout and four-year graduation. 2.2.3. Other covariates Our analysis includes other student attributes that may be associated with the key outcome of this study directly and in some instances through their association with the registration process, including course shutouts. For example, students completing college credits prior to arriving at UC Davis (through advanced placement courses or dual enrollment) need fewer credits earned while at UC Davis to graduate, are assigned to higher registration priority groups and may have shorter time to degree than students who enter with zero credits. As a result, we include a measure for the number of units a student has upon entry at UC Davis. From extant literature we know other demographic characteristics may impact students’ likelihood of graduation and time to degree. These include: race/ethnicity, gender, parental education and income, and prior academic achievement (Bradburn, 2003; Bound, Lovenheim & Turner 2010a, 2010b, 2012). Finally, we also

9 Results are robust to other methods of pulling in the outliers on shutouts. Omitting the top 1 percent of shutouts results in a loss of 172 students. Including these students in the analysis also did not impact the overall findings.

include a measure for freshmen year fall advantage (that is, students who have an advantage by showing up to an earlier summer orientation session for registration prior to the fall term). We measure that freshmen registration advantage as the proportion of freshmen registering after a given student in the fall term of year one. Although the fall registration time is not randomly assigned, it may impact course choices in the first year and therefore in subsequent years. Table 2 presents the descriptive statistics for both the full sample of first-time freshmen, and the analytic samples. Over half of all first-time freshmen at UC Davis had at least one parent who received a college degree, were likely to be white or Asian, and have an average high school GPA of 3.74. It is interesting to note that the average firsttime freshmen student earned about 12.4 college units before beginning at UC Davis, which is a little more than a full term (12 units). 2.3. Methods We fit OLS models to determine if course shutout has an impact on student time to degree: TTDi ¼ b1 SHUTOUTSi þ ei

(1)

where 4YGRADi represents the time to degree for individual i. SHUTOUTSi represents the average number of course shutouts experienced per term over the first four years for student i, and ei is the error term (in this baseline model we also include cohort fixed effects). We fit both logistic regression and linear probability models for the binary outcome graduating in four years (4YGRAD). We next add a vector of covariates Xi to Eq. (1) to get: TTDi ¼ b1 SHUTOUTSi þ g X i þ ei

(2)

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M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39 Table 2 Comparison of analytic samples.

N 4YGRAD Average Shutouts (4 Years) Female Male Asian Hispanic Black Other Ethnicity White Parent Ed Less than College Parents Some College Parent Bachelors Degree Parent Post-Baccalaureate Parent Missing Education Private HS HS GPA HS GPA Missing Parent Income (Log) Parent Income Missing Units at Entry Freshman Luck Advantage College of Agriculture College of Engineering College of Letters and Sciences Cohort Fall 2002 Cohort Fall 2003 Cohort Fall 2004 Ever High Priority Registration Ever use Summer Term Double Major Switched Major Major Undeclared at Entry

All students

Analytic samples 4YGRAD

TTD

13,725 0.567 3.99 0.565 0.435 0.330 0.109 0.024 0.158 0.380 0.216 0.156 0.238 0.353 0.037 0.134 3.73 0.001 10.9 0.214 12.0 0.011 0.245 0.124 0.631 0.340 0.349 0.311 0.174 0.656 0.136 0.441 0.343

9780 0.581 3.87 0.564 0.436 0.358 0.085 0.012 0.160 0.384 0.197 0.145 0.249 0.371 0.039 0.141 3.74 0.001 11.0 0.226 12.4 0.150 0.239 0.131 0.630 0.349 0.344 0.307 0.000 0.710 0.162 0.408 0.337

9274 0.613 3.86 0.570 0.430 0.358 0.082 0.012 0.160 0.388 0.195 0.144 0.248 0.374 0.039 0.142 3.75 0.001 11.0 0.228 12.5 0.163 0.239 0.129 0.632 0.349 0.344 0.307 0.000 0.707 0.170 0.393 0.339

Notes: 4YGRAD sample excludes students who received special registration priority, as well as students who exit the university before spring of their fourth year. TTD sample excludes the same students, as well as students who did not graduate within our data window.

The covariates included in g are the following student characteristics: gender, race/ethnicity, parent education levels, parent income, private/public high school, high school GPA, number of units earned before freshman year, and fall freshman registration advantage; we also include cohort and major college fixed effects. Again, we fit similar logit and linear probability models for 4YGRAD. For all models we account for heteroskedasticity by adjusting our standard errors. 2.3.1. Identifying exogenous variation in course shutouts Students may have different strategies when trying to enroll for classes, and much of the process is unobserved by researchers. Students have access to a real-time list of available and full courses when they are logged into the online registration system. Since many students may plan their schedules according to the list of courses and sections that are already full, our measure of course scarcity is potentially endogenous with other registration behavior that we do not observe. For example, some students consult online resources regularly before registration to identify courses that still have openings, and therefore may not experience course shutouts via registration. Students that have more degree requirements, those who might want to take smaller classes, classes at specific times of the

day, or classes with certain instructors may also experience shutouts at higher rates than those that do not. We address this potential endogeneity by employing an instrumental variables approach. As previously noted, shutouts do not occur randomly; therefore an analysis of their effect on graduation using Eq. (1) or (2) may be biased. We utilize the University’s registration process and the exogenous variation in the randomly assigned registration times as an instrumental variable through which we can estimate an unbiased effect of shutouts on BA completion in four years. Random registration time assignment is an ideal instrument here in that it causes some of the variation in course shutouts. Using a standard Instrumental Variable (IV) approach, we use the portion of the variation in shutouts that is exogenous and then rely on that exogenous variation to estimate the effect of shutouts on our outcomes—TTD and 4YGRAD. We first provide a brief explanation of the registration process (additional details are available in Appendix A). All students are assigned priority groups for registration based on their accumulated credits. Within these priority groups, students are assigned registration times that are determined at random. Students who obtain an earlier registration time in their priority groups are more likely to have open courses than students who register later in the

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39

2 0

1

Density

3

Unlucky (Bottom 10%)

4

31

0

.2

.4 .6 Cumulative luck across 4 years

.8

1

kernel = epanechnikov, bandwidth = .02

Fig. 4. Cumulative luck distribution for all first-time freshmen. Notes: The distribution of cumulative luck from the second term through the final term of the fourth year (12th term).

priority group. Based on the randomization of registration times within priority groups, we consider a student who receives a favorable registration time as lucky, and a student who receives the unfavorable registration time as unlucky. The sizes of priority groups differ some from term to term, but the median size of a priority group is about 900 students; thus, students who are randomly assigned to the group of about 80 students with the first registration time in each priority group (i.e. the luckiest students) have the opportunity to register before about 820 of her peers in their same priority group. Consequently, the students assigned to the last registration time (i.e. the unluckiest students) in the priority group must register after about 820 other students in their priority group. We define registration luck for Student A in a particular term as the proportion of students within Student A’s priority group registering after Student A. We calculate a measure of cumulative luck for each student by averaging the luck in each term over a student’s first four years. We exclude fall freshmen registration because of its nonrandom nature. We offer a more detailed description of fall freshmen registration in Appendix A. Since the withinpriority group registration time is assigned at random, students will tend to break even over repeated draws (i.e., across terms of enrollment). However, some students will have repeatedly early or late draws simply by chance. Based on cumulative luck we define a dichotomous measure of unlucky registration times by distinguishing students who are consistently extremely unlucky (students in the bottom 10 percent of the cumulative luck distribution).10 We use the accumulated number of

10 We do test whether luck is randomly distributed; although some student characteristics are significantly related to luck, the coefficients capturing these relationships are trivial in magnitude.

shutouts and the accumulated luck across four years for two reasons. First, our main goal is to see if in this institution, course scarcity results in a longer time to graduation. Second, any one term of bad luck or a high number of shutouts alone, is not likely to have a major impact on a student’s four-year career at a university. Consistently poor luck, however, is more likely to have a negative impact. Fig. 4 shows the distribution of luck for all first-time freshmen and the cutoff for the bottom ten percent of students. A student is extremely unlucky if, on average over four years, 37 percent or less of a student’s priority groups register after her. Students who receive an occasional bad luck draw are not likely to suffer due to only being behind 800 or so students on occasion, but those with repeated bad draws could see marginally cumulative effects of later registration times. Luck is included in our models as a dichotomous measure— UNLUCKY— indicating whether a student is extremely unlucky (i.e. in the bottom 10 percent of cumulative luck over the first four years) or not.11 We use two-stage least squares (2SLS) estimation to fit the following statistical models: 1st stage : SHUTOUTSi ¼ d1 UNLUCKY i þ ei

(3)

d 2nd stage : TTDi ¼ b1 SHUTOUTS i þ mi

(4)

11 We test the results with several different specifications of the instrument, including dichotomous variables representing each of 5 percent, 10 percent, and 15 percent of the unluckiest students, as well as a continuous measure for luck. The first stage results suggest that the continuous measure is too weak of an instrument to be useful (these additional specifications can be obtained from the author).

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39

.1 0

.05

Density

.15

.2

32

0

5

10 x 4YGRAD=1

15

20

4YGRAD=0

Fig. 5. Distribution of average shutouts per quarter by on-time graduation status. Notes: Kernel density plots of the distribution of average shutouts per term over a student’s first four years. Students with the top one percent of shutouts omitted.

In the first-stage model, we regress shutouts on our measure of how unlucky students are with regard to their course registration timing. In the second-stage model, we regress our outcome (TTD) on the predicted shutouts obtained from the first-stage model. Regression parameter b1 represents the time to degree for student i as a result of course shutouts. The IV approach carves out the variation in course shutouts that is random with respect to the outcome. Thus, because the predicted values of SHUTOUTS from the first-stage equation include only the variation in SHUTOUTS that is caused by the instrument, UNLUCKY, the estimated coefficient from the second-stage equation will be unbiased. We also include cohort and college-level fixed effects to control for potential differences that may exist across cohorts (e.g., size), and to capitalize on the variation in shutouts after controlling for the college-level characteristics that may be constant across all students. Lastly, as with the first OLS models, we add other controls that may be associated with either our outcome of interest and course shutout. We next evaluate the instrument by determining whether the assumptions for IV hold. First, although we cannot prove that luck only affects four-year graduation through its impact on shutouts (the exclusion restriction), given that registration luck is solely about luck in obtaining students’ desired courses, we can think of no other potential path to influencing on-time graduation. Second, we can confirm that our instrument is ignorable (i.e., randomly assigned) through both administrative channels at the University and our own descriptive analysis. Finally, we demonstrate that luck does have an effect on shutouts, but that this instrument is somewhat weak (F-stat = 8.06). Students who are consistently unlucky have, on average, more shutouts per term than their more lucky counterparts, a difference of .53 (s.e. = .1922)—about half of a course per term. Results from the first stage are presented in Table A3.

3. Results Students who graduate in four years have fewer average shutouts per term (3.67) than those who graduate in more than four years (4.03). Fig. 5 plots the distribution of average shutouts by our outcome status (on-time or not). From this plot, we note that, on average, students who graduate in four years experienced fewer average shutouts. We present the results from the set of regressions for graduation in four years in Table 3. Column 1 presents the unadjusted OLS models, in column 2 we add covariates, and in columns 3 and 4 we report results from the IV models, without and with covariates, respectively. OLS results in columns 1 and 2 show that the more course shutouts students experience the lower the likelihood of graduating in four years. The effect is small (roughly one percentage point), statistically significant, and persistent upon control for a variety of covariates. Results from our IV estimates, however, suggest that course shutouts do not impact on-time graduation. Table 4 presents results from these same models applied to predicting time to degree. We again note small, but statistically significant effects of course shutouts on TTD; an additional course shutout is associated with a 3 percent of one term increase in TTD in the unconditional model, and this estimate is reduced to about 0.2 percent of one term in the model with covariates. However, results from our IV estimates suggest that more shutouts do not result in a longer time to degree, which is consistent with the IV results regarding on-time graduation. Results are robust to alternate specifications of the luck instrument, specifically the 10 percent and 15 percent of the unluckiest students and continuous luck.12

12

These results can be obtained from the author.

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39 Table 3 Regression results for the impact of shutouts on on-time graduation. Model

1 OLS

2 OLS

3 IV

4 IV

Average Shutouts (s.e.) Covariates Cohort Fixed Effects College Fixed Effects

0.010*** (0.002) N N N

0.008*** (0.002) Y Y Y

0.083 (0.067) N N N

0.173 (0.124) Y Y Y

Notes: Outcome is 4YGRAD, and average shutouts represent the average shutouts per term across a student’s first four years. Covariates include: gender, race, parent education level, parent income, whether student attended a private high school, high school GPA, number of college units earned prior to entry to the university, college upon entry to the university, and freshman fall registration time. The IV models include a consistently unlucky registration time as an instrument for average shutouts per term. * p < .05. ** p < .01. *** p < .001.

Table 4 Regression results for the impact of shutouts on time to degree. Model

1 OLS

2 OLS

3 IV

4 IV

Average Shutouts (s.e.) Covariates Cohort Fixed Effects College Fixed Effects

0.031*** (0.006) N N N

0.019** (0.007) Y Y Y

0.271 (0.244) N N N

0.775 (0.516) Y Y Y

Notes: Outcome is TTD, and average shutouts represent the average shutouts per term across a student’s first four years. Covariates include: gender, race, parent education level, parent income, whether student attended a private high school, high school GPA, number of college units earned prior to entry to the university, college upon entry to the university, and freshman fall registration time. The IV models include a consistently unlucky registration time as an instrument for average shutouts per term. * p < .05. ** p < .01. *** p < .001.

4. Discussion There could be a number of explanations for the substantively zero findings of the impact of course shutouts on four year graduation and time to degree. How might students respond to course scarcity? In this section we elaborate on several possible explanations for the results we present. In particular, we disentangle a variety of forces that may be associated with course scarcity. We discuss evidence on whether students are responding to course scarcity by taking fewer courses or perhaps by taking the wrong courses. We also discuss what student characteristics and actions are associated with ontime graduation. Students who do not get into the courses they want may simply take fewer classes in those terms. In Fig. 6, we plot the marginal effects from an OLS model regressing units accumulated on number of shutouts by term (for the first four years of students’ postsecondary study). We see that, in fact, the relationship between shutouts and credits accumulated in a given term is not consistently negative.

33

Early in a student’s postsecondary career they are likely focusing on general education course requirements, with potentially much flexibility in choosing courses, and therefore a shutout may not lead to fewer courses taken. Toward the middle of a student’s college career, however, the relationship between course shutouts and units accumulated can be negative, though it is trivially small (one additional shutout is associated with a .035 of a unit), suggesting that any effects of shutouts may only be measureable when accumulated over multiple years. It is interesting to note that in some quarters the relationship is actually positive, more shutouts are associated with more units. This may not be surprising since the more courses a student takes the more slots they have to fill, and therefore the more likely they may be shut out of at least one of them. Though again the relationship is trivially small (note the effects in later terms, such as the 12th term, can be misleading because very few shutouts occur by the 12th term (on average only about 1.9)). Overall, we find no evidence of slow credit accumulation on account of course shutouts, suggesting that students find suitable substitutes for courses that are full. Students who experience more shutouts may also simply be more likely to leave the University all together. College exit is a rare event for our sample. Only 4.3 percent of students in our sample do not return for their second year at UC Davis (or at another point during the period under investigation). However, by the third year, we see about a 10 percent departure rate.13 Given that the majority of shutouts that students experience occur earlier in their time at UC Davis, it is distinctly possible that shutouts may discourage students, the result of which could be college departure. Descriptively, we note higher average rates of course shutouts among those that do exit the University, when compared to those who stay; a difference of about 1.4 in year one and a difference of about 1.8 in year one and two. Among the 489 (4.31 percent) of first year students from our three cohorts combined who did not return for year 2, they experienced an average of 5.79 shutouts, as compared with those who persisted, which experienced an average of 4.35 shutouts. Among the 1085 (9.57 percent) of students from our three cohorts combined who did not return for year 2 or 3, they experienced an average of 5.90 shutouts, as compared with those who persisted, which experienced an average of 4.09 shutouts. Unfortunately, our sample does not lend itself well to explorations of college departure given the low occurrence. Nevertheless, to the extent that the registration process at UCD is highly generalizable to other large public four-year institutions, it is important to consider the extent to which course scarcity may contribute to college departure—a critical area of investigation among more open-access postsecondary institutions. While it seems clear that students are not taking fewer courses as a result of more shutouts, students could be responding to course shutouts by taking the wrong courses

13 It is important to note that these college departures are not necessarily non-degree recipients; it is likely that those who left UC Davis transferred to another postsecondary institution.

.1

8

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39

34

7.6

4.9

Effect Size

5

4

3.9 3 2.7 1.8

1.9

11

12

-.05

2

2

0

2.7

Average Shutouts

.05

6

6.2

2

3

4

5

6

Effect Size

7 Term

8

9

10

Average Shutouts

Fig. 6. Association between one additional shutout on units earned (by term). Notes: Effect sizes are coefficients from a linear probability model regressing units earned by a student on shutouts for that student (in a particular term). Terms 12 and 4 are statistically significant at the a < .05 level. The average shutouts per term are the average number of shutouts for all three cohorts of students in that particular term.

(i.e., those that may be different than their intended path). It is difficult to test whether a student is enrolling in the right or wrong courses, because a student’s degree intentions are not clear from our data, nor are they necessarily static. While it is challenging to empirically test whether a student is taking the wrong courses, it is possible that we can observe student behaviors that may result from taking the wrong courses as a result of course scarcity. For example, if students are taking the wrong courses during the school year, they may need to take the right courses during the summer. Seventy percent of all UCD students participate in summer school at least once during their first four years of study. In fact, these students also, on average, experience more shutouts during these four years than students who do not participate in summer school. The average shutouts experienced among those that do utilize summer school is 4.06, compared to 3.21 for students who do not. Although these are small and descriptive, it is quite possible that summer school attenuates for increased time to degree that may be, at least partially, the result of course scarcity. It is also possible that extra courses may lead some students to change their major, either because they get discouraged by their inability to obtain the courses needed for their intended major, or they may decide to take a different path through their experiment taking unintended courses. Over 40 percent of all freshmen graduate with a different major than the one they started with at the university. These students, on average, experience more shutouts over their first four years when compared to students who never switch majors, a difference of about one-half of a course. However, these descriptive findings can be somewhat misleading in that the students who switch majors likely require more courses to meet the new major’s course requirements, leading them to experience more

shutouts. The reverse causality problem suggests these relationships should be interpreted with great caution.14 Finally, it is also possible that some majors are more likely to be impacted by course scarcity than others. Students in majors with flexible course requirements, or more room for electives, may be able to fulfill the requirements despite being shut out of full courses, while students in majors with rigid requirements or strict course series may be more likely to be affected by course scarcity. We include these (and other characteristics about individuals) as covariates in our models and note that, while they do influence our outcome of interest (on-time graduation and time to degree), they do not fundamentally change the relationship between course shutout and our outcomes. (Full model coefficients are available in Tables A1 and A2.) Controlling for a variety of other student characteristics, students who enroll in summer school, change their major or are undeclared when they come in, are less likely to graduate on time (Table A1, column 3) and have longer time to degree (Table A2, column 3). Interestingly, double-majoring is associated with on-time graduation and shorter time to degree. We also note that the average student who enters the College of Engineering is about 8 percentage points less likely to graduate in four years when compared to the average student who enrolls

14 Similarly, course shutouts may also lead students to take enough additional courses that they decide to double major. We find little descriptive evidence of this. Fewer than 20 percent of students graduate with more than one major and these students on average have lower average shutouts. Again we note the reverse causality problem here; students who double major require more specific courses, which can lead to more shutouts. Nevertheless, while switching majors or double majoring itself may cause a lengthier time to degree, descriptive data suggest that course shutouts are not driving these differences.

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39

in the College of Letters and Sciences (the omitted reference group); and, the average student who enters the College of Agriculture is about 2.7 percentage points more likely to graduate in four years when compared to the average student who enrolls in the College of Letters and Sciences. Importantly, and for the objective of this paper, we note the minimal influence of these covariates on our key predictor—course shutouts. It is clear that course scarcity at this university has, at most, a very minor impact on on-time graduation, and likely no substantive impact. We do, however, find several other student characteristics and actions that may influence time to degree and on-time graduation (full model results available in Tables A1 and A2). First, corroborating a variety of correlational studies, several key demographic characteristics appear to be associated with time to degree. Controlling for other student characteristics, females graduate more than half of a term earlier than males. Black and Hispanic students take longer to graduate than white students (5.4 terms longer and 3.7 terms longer, respectively). In addition to race/ethnicity and gender, previous academic characteristics of students are also key determinants of time to degree. Students with higher GPAs in high school and students who complete more college units while in high school graduate sooner. A student who enters UC Davis with the mean number of units in our sample (12) will likely graduate about one third of a term earlier than a student who enters with no units, all else equal. We expect this for several reasons: (1) students who enter the university with college credit may need to take fewer courses to graduate, and (2) because the overall registration process advantages students who enter the university with more credits.

35

In this paper we explore a ubiquitous aspect of college enrollment at many large public four-year institutions— course scarcity. We utilize unique administrative audit data to measure course shutout and to utilize randomized course registration times at a large public flagship university. We find that course crowding does not impact the time it takes for students to earn a degree. While scarce per-pupil resources may cause students to delay graduation in some instances, its main mechanism may not be through the crowding out of courses. Thus, even though students are crowded out of courses and time to degree remains a concern for many universities, course crowding does not appear to result in degree delays at UC Davis. Whether this is because of more flexible majors, good counseling, or perhaps the fact that the University is on a quarter—rather than semester—system, is all open for discussion and further empirical work. This study also provides a critical venture into the black box of institutional practices that might influence postsecondary outcomes. Students at UC Davis repeatedly reported in surveys that they could not get the courses they want in order to graduate in a timely way. However, our analysis provides compelling evidence from very detailed data on students’ actual behaviors, which suggests otherwise. Despite anecdotes or widely held beliefs about course constraints, the common practice for distributing opportunities for course registration at one large public four-year university, may not influence students’ postsecondary completion trajectories. As such, this analysis also offers an important application of detailed individual-level data that many campuses collect, and which can provide key new insights about how institutional policies, programs and practices can influence a variety of student outcomes.

5. Conclusion Despite considerable speculation about why some public four-year colleges and universities are more successful at graduating students ‘‘on-time’’ there is very little direct evidence of how specific institutional policies affect college completion or time to degree. Previous work to explain the variation in degree attainment and time to degree has primarily focused on individual determinants. We know much less about institutional explanations. Recent studies suggest institutional constraints and resources may play an important part, particularly at less selective campuses, in explaining increased time to degree (Bound et al., 2012). Why should we be concerned with the apparent rise in time to degree among college-goers? From the institutional side, increased time to degree can lead to cohort crowding, spreading scarce resources more thinly across students or preventing the institution from accepting additional students, and a host of complications in planning or course scheduling. Of course, individuals also bear great costs in delaying entry into the workforce, starting with the increased financial cost to schooling through additional years of tuition.15

15

Alternatively, students may be accruing more human capital while in school longer.

Appendix A. Course registration at UC Davis Undergraduate course registration at UC Davis occurs in three main stages: Pass 1, Pass 2, and open registration. The first stage of registration for any quarter, termed ‘Pass 1,’ begins about five weeks into the preceding quarter. Pass 1 lasts for approximately three weeks, and students are allowed to register for up to 17 units.16 In Pass 1 students are assigned to groups of registration appointment times— called priority groups—based on their cumulative completed credits. Students with more credits are in earlier priority groups. There are 15 priority groups containing different numbers of students based on the number enrolled in a given quarter and the concentration of students within each credit range. The median priority group contains about 900 students, though depending on the quarter some of the earliest priority groups can contain as few as 300 students and some of the latest priority groups can contain up to 1800 students. Within priority groups, each student is randomly placed in a subgroup of about 80 students, and that subgroup is

16 The expected undergraduate load for a quarter is 15 units; 12–13 is the average. Prior to Fall 2005, the upper limit for units in Pass 1 was 13.5 units.

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39

36

Fig. A1. Registration process at UC Davis.

given a 4-h registration window. All students within an earlier priority group have assigned times before students of the next (later) priority group. After all students have had a chance to register during Pass 1, Pass 2 begins, and follows the same pattern. Once the quarter begins, students may still adjust their schedules by adding and dropping classes until the tenth day of instruction. There is no assignment of registration windows during open registration. Both Pass 1 and Pass 2 rely on the randomly generated registration windows for students. The last stage, open registration, allows students to register at any time, and all three are shown in Fig. A1. Within Pass 1 and Pass 2, students receive a 4-h window of time to register for their courses for the next quarter. Each 4-h window begins 30 min after the previous 4-h window, and that pattern continues until the entire priority group has an opportunity to register. The staggered pattern of assigned registration windows leaves students with an advantageous 30 min registration period before the next group has the ability to register. About 90 percent of students use their 4-h Pass 1 appointment window, but only 60–80 percent of students do so in the initial half hour. A student who wishes

10am 11am

to adjust his or her schedule after their window may do so on any evening or weekend after their appointment time has passed (Fig. A2). Fall registration for entering students is structured differently from the other registration periods. All freshmen register during their summer visit to the University. These visits happen throughout the summer, and the different colleges invite their students to visit the campus at different times. Students may choose from available visit dates for their college. We include a measure for the order in which students registered for courses in the fall of their freshman year in all of our models, but not as a part of the random registration time. Students likely select into earlier or later fall freshman visit times for different reasons. This measure may be a proxy for parental involvement, as parents are encouraged to visit in the summer with their students. This variable may also be a proxy some other factor related to eventual graduation such as motivation (more motivated students may be the first to sign up), financial situation (having to work around a job schedule to visit), or proximity to the university. This variable is related to on-time graduation. On average, a one standard deviation difference

Priority Group 10 Priority Group 11 . . . subgroup 14 subgroup 15 subgroup 1 subgroup 2 ... ~80 students ~80 students ~80 students ~80 students

12pm 1pm 2pm 3pm Fig. A2. Appointment windows for a hypothetical group of students in priority groups 10 and 11.

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39

37

Table A1 Full regression results for 4YGRAD on average shutouts. Model

1 OLS

2 OLS

3 OLS

4 IV

5 IV

Average Shutouts

0.010*** (0.002)

0.008*** (0.002)

0.006*** (0.002)

0.083 (0.067)

0.173 (0.124)

0.147*** (0.010) 0.010 (0.012) 0.081*** (0.019) 0.142** (0.045) 0.006 (0.014) 0.018 (0.017) 0.001 (0.016) 0.010 (0.016) 0.018 (0.029) 0.010 (0.014) 0.211*** (0.016) 0.008 (0.187) 0.020*** (0.006) 0.031** (0.012) 0.004*** (0.000) 0.060*** (0.007)

0.144*** (0.010) 0.022* (0.012) 0.082*** (0.019) 0.150*** (0.043) 0.015 (0.014) 0.016 (0.017) 0.002 (0.016) 0.011 (0.016) 0.024 (0.028) 0.010 (0.014) 0.206*** (0.016) 0.000 (0.178) 0.020*** (0.005) 0.033** (0.012) 0.004*** (0.000) 0.051*** (0.006)

0.003 (0.104) 0.141 (0.104) 0.116** (0.036) 0.162** (0.061) 0.128 (0.095) 0.055 (0.056) 0.076 (0.058) 0.066 (0.058) 0.095 (0.087) 0.035 (0.026) 0.274*** (0.050) 0.229 (0.268) 0.048** (0.020) 0.050** (0.022) 0.011** (0.005) 0.071*** (0.012)

0.019 (0.014) 0.062** (0.019) 0.032** (0.011) 0.029** (0.012)

0.027** (0.014) 0.078*** (0.019) 0.039*** (0.011) 0.032** (0.012)

0.050* (0.029) 0.024 (0.064) 0.112** (0.057) 0.115* (0.061)

0.264 (0.256)

1.844** (0.896)

. 9780

. 9780

Covariates Female Asian Hispanic Black/African American Other Ethnicity Parent Some College Parent BA Parent Post-BA Parent Educ Missing Private HS HS GPA HS GPA Missing Parent Income (Log) Parent Income Missing Units At Entry Freshman Luck Advantage

Major College (Arts and Sciences-Ref) College of Agriculture College of Engineering Cohort Fall 2003 Cohort Fall 2004

Student Actions Summer School

Constant

0.619*** (0.008)

0.546*** (0.084)

0.035** (0.011) 0.069*** (0.013) 0.149*** (0.012) 0.117*** (0.012) 0.424*** (0.084)

r2 N

0.003 9780

0.098 9780

0.117 9780

Two Majors Major Switch Undeclared

* p < .05. ** p < .01. *** p < .001.

38

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39

Table A2 Full regression results for time to degree on average shutouts. Model

1 OLS

2 OLS

3 OLS

4 IV

5 IV

Average Shutouts

0.031*** (0.006)

0.019** (0.007)

0.014** (0.007)

0.271 (0.244)

0.775 (0.516)

0.554*** (0.039) 0.039 (0.045) 0.304*** (0.077) 0.295* (0.153) 0.048 (0.053) 0.016 (0.065) 0.013 (0.060) 0.031 (0.061) 0.094 (0.106) 0.044 (0.049) 0.719*** (0.065) 0.845 (0.773) 0.089*** (0.023) 0.100** (0.043) 0.021*** (0.002) 0.208*** (0.026)

0.541*** (0.039) 0.041 (0.045) 0.325*** (0.076) 0.340** (0.150) 0.049 (0.052) 0.033 (0.065) 0.010 (0.060) 0.019 (0.060) 0.095 (0.105) 0.047 (0.049) 0.723*** (0.065) 0.779 (0.739) 0.089*** (0.023) 0.108** (0.043) 0.020*** (0.002) 0.183*** (0.026)

0.105 (0.434) 0.601 (0.420) 0.451** (0.153) 0.434* (0.259) 0.548 (0.399) 0.356 (0.247) 0.358 (0.265) 0.315 (0.249) 0.420 (0.371) 0.143 (0.104) 1.006*** (0.217) 0.176 (1.132) 0.210** (0.084) 0.163** (0.083) 0.051** (0.020) 0.258*** (0.053)

0.080 (0.052) 0.193** (0.075) 0.121** (0.045) 0.323*** (0.042)

0.105** (0.051) 0.250** (0.077) 0.146** (0.045) 0.356*** (0.043)

0.233* (0.129) 0.194 (0.274) 0.483** (0.246) -0.705** (0.259)

13.899*** (0.928)

22.939*** (3.771)

. 9274

. 9274

Covariates Female Asian Hispanic Black/African American Other Ethnicity Parent Some College Parent BA Parent Post-BA Parent Educ Missing Private HS HS GPA HS GPA Missing Parent Income (Log) Parent Income Missing Units Entry Freshman Luck Advantage

Major College (Arts and Sciences-Ref) College of Agriculture College of Engineering Cohort Fall 2003 Cohort Fall 2004

Student Actions Summer School

Constant

12.749*** (0.030)

17.193*** (0.349)

0.058 (0.039) 0.214*** (0.043) 0.463*** (0.042) 0.372*** (0.043) 16.999*** (0.349)

r2 N

0.003 9274

0.111 9274

0.125 9274

Two Majors Major Switch Undeclared

* p < .05. ** p < .01. *** p < .001.

M. Kurlaender et al. / Economics of Education Review 41 (2014) 24–39 Table A3 First stage regression results. Outcome

Unlucky Constant r2 N F

First stage

Reduced form

Reduced form

Shutouts

Four year graduation

Time to degree

0.285** (0.105) 3.796*** (0.031)

0.024 (0.016) 0.578*** (0.005)

0.066 (0.054) 12.875*** (0.020)

0.001 9780 7.32

0.000 9780 2.03

0.000 9368 1.45

* p < .05. ** p < .01. *** p < .001.

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