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A MODEL OF THE DETERMINANTS OF TTD The theory developed in this chapter is based largely on an opportunity- cost explanation of student choice and is concerned primarily with direct, rather than indirect, effects. The chapter begins with a discussion of five vectors that belong in a model of student choice and then explores the opportunity-cost arguments underlying the choice of variables. The ways in which financial aid affects time to completion and the role of market forces (relative salaries and employment opportunities) also are examined. A discussion of the variables used in the model is included. The Model TTD is directly affected by five vectors of variables similar to those shown to influence demand for graduate school and persistence to the degree: family background characteristics (F), individual abilities and interests (I), tuition and financial aid (TLFA), environment and policies of institutional organizations (O), and economic and social forces (E).7 The relation is: (1) ~ iL)dt = fd(Fd~t-n), Id~t-n), TLFAd~t-n), d~t-n), Ed~t-n)) In the formula, "dt" denotes the field (d) and the year (t) in which a given cohort of doctorates received Ph.D.s. Since the model is used to explain changes in TTD in 11 fields and many of its variables affect iced several years before a cohort receives the doctorate, a cohort that received its doctorate in year "t" is assumed to have been affected by the variables in the five vectors "n" years prior to the time that the degree was completed (although not acknowledged in Equation 1, the "n" may be different for each variable and also for each field). 7 The model can be formulated in path-analytic terms by having F affect 0, I, and E and by considering the indirect effects of E on 0, TLFA, and F. 35

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The doctorate cohort (i.e., those receiving their Ph.D.s in a given year) is used as the unit of analysis, although the model is equally applicable using an individual as the unit of analysis. Variables in the "F" vector include the percentage of the cohort that is married and average t number of dependents. The "I" vector includes student attributes such as average age and grade-point average. "TLFA" is comprised of variables such as the cohort's average tuition and the percentage of the cohort receiving financial aid. The "O" vector contains information on the undergraduate and graduate schools their average quality, government spending on R&D, and the percentage of foreign baccalaureates enrolled attended by persons in the cohort. "E" vector variables relate to the average starting salaries of new doctorates, the relation of doctorate to nondoctorate salaries, and the relation of salaries of new doctorates to those already in the field. Variables that capture the employment and unemployment experience of new and recent doctorates also are included. Since the cohort is the unit of analysis, variables on faculty-student interaction and social and academic integration are not included in the time-series version of this model.8 The Critical Role of Opportunity Costs The model assumes opportunity costs affect student decisions that impact on ~D, but it does not explicitly allow for institutional decisions. From an economic perspective, a student's decision to undertake and complete a doctoral program involves a set of near-term costs in the form of opportunities foregone while the student pursues the doctorate. Current costs are borne in anticipation of future benefits, and both the costs and the future returns from the doctorate include monetary and nonmonetary elements. There are at least three cost elements for graduate students, but they do not all affect TTD in the same way. As foregone earnings increase, TTD should decrease as pressure on students to enter the job market and earn an income rises. As foregone activities (e.g., work activities such as employment as a teaching assistant) increase, study time should decrease, with ITD increasing as a result. As financial outlays (primarily tuition) increase, incentives are created to finish 8 Changes in programmatic requirements can 'elongate HID: increasing the number of courses required for completion, requiring students to acquire additional competencies, lengthening time spent on doctorate-related research, andior increasing the work experience that students must have to be eligible for the degree. Careful examination of these requirements would involve a separate study. 36

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school as quickly as possible, and ICED decreases. Thus, student aid is expected to have both positive and negative effects on IBID, and those effects tend to be offsetting. As a result, the nature of the net effect (i.e., positive or negative) cannot be stated a priori. Each vector in the model can be examined within the opportunity-cost framework. Other things equal, there will be a positive relationship between these costs and TTD. For example, it can be argued that married students have fewer costs associated with study time than single students. Since the opportunity costs of study time are often greater for single than married students, other things being equal, single students will spend less time on study and will have a high MID. An opportunity-cost argument can also be made for the effects of family size. Other things remaining equal, as the number of dependents increases, the amount of time the student spends with the family also increases, causing TTD to rise. To the extent that women take primary responsibility for child rearing, married women with children will have a higher TID than will married men with children. Students who are better prepared to deal with the subject matter of their dissertation may find it less costly (in terms of time and effort required) to work on the doctorate. And it follows that students with an undergraduate degree in the same field as their doctoral study will, on average, have lower costs than those with a degree in a different field. Likewise, for those who enter graduate school with a high ORE score in the doctoral field, less time, and therefore less expense, probably will be needed to acquire the degree. The effect of the quality of undergraduate education on ITD is not easy to assess. Study at a high-quality undergraduate institution may increase a student's preparation for graduate school, reducing the cost of pursuing the doctorate and resulting in faster progress to the degree. But attending a high- calibre institution can also lead to Davis' (1966) "frog pond" effect in which student expectations and grades drop, which in turn may increase AID. The graduates of frog ponds may take their reduced expectations to graduate school, causing them to take longer to complete the doctorate. Also not obvious is how quality of institution at the graduate level affects TID. On the one hand, higher-quality institutions may provide their students with greater academic, social, and intellectual integration than lower- quality institutions and may be more efficient educators. Both phenomena reduce the costs of pursuing the doctorate, lower the costs of study time, and lower 1-1~. On the other hand, high-quality graduate schools may also impose more rigorous academic requirements on their doctoral candidates, requiring more research and study, with the ultimate effect of increasing TID. Market forces operate within the opportunity-cost context by determining what purchases the student foregoes while studying for a degree and 37

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what he or she can hope to receive in the future. The relationship between market forces and completion times is discussed later in this chapter. Financial Aid and Its Impact on Completion Times The Impact of Type of Aid Because it offsets some of the income lost by being in school, financial aid in the form of fellowships, grants, and/or stipends reduces the opportunity costs of pursuing the doctorate. The pressure on students with aid to find outside employment is lessened, and they are freed to work on degree-related activities. Aid that replaces a large amount of foregone income creates an incentive for some students to substitute leisure activities rather than study time for non- degree related work. Other students may increase TTD by enlarging the scope of their dissertation or taking an extra course or two. Although for many students financial aid is likely to increase their full-time work toward the doctorate, the net effect of fellowship aid on time to completion depends on whether students are more likely to partake in leisure or study activities when an award is made.9 Student behavior may also be affected if fellowship aid is contingent on a showing of successful progress toward the degree. The more stringent the criteria for demonstrating progress, the less likely students are to substitute leisure activities for study. However, it may be difficult to define "successful progress," since such criteria are fairly subjective (Prior, 1962~. Those with fellowships take less time to complete the degree than do recipients of teaching assistantships or those without aid, perhaps in part because they are more intellectually able. Students with teaching assistantships as their primary source of support have a lower opportunity cost for study than those who must support themselves through graduate school. Teaching assistants (TAs), because their aid package is dependent on the performance of services that take time away from doctorate-related activities, do not have as much time available for study as fellows or research assistants (RAs), suggesting Ida) for the average TA will be longer than for the average fellow. The situation with research assistantships is less clear. The wide range of duties assigned to RAs makes it difficult to generalize about the effects of such awards upon l-lL). Those engaged in research related to their doctorate do not really give up study time when they spend job time in a way that facilitates 9 For that matter, it also depends on whether the faculty who supervise dissertations have a preconceived idea of how long a dissertation should take, on university policies, and on curriculum matters. 38

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completion of the doctorate. In contrast, those engaged in work unrelated to the doctorate may find that their job slows their progress toward the degree. The opportunity-cost approach explains why students using their own earnings as the primary source of support are likely to take longer to complete the degree. A student employed full-time in a nondoctorate-related job must decide how to allocate non-work hours among leisure, study, family-related, and other activities. On average, the theory suggests, the time a working person devotes to doctoral study will be less than the time spent by those with teaching or research assistantships or fellowships. A 1987 study by Abedi and Benkin found that mean TTD and mean RTD are over two years longer for students using their own earnings as a primary income source than for those whose money comes from other sources. But this same study found TTD was lower for students with "on-campus" earnings (including TAs and RAs) than for those with fellowships and grants. This fading is not consistent with the theory that AD decreases as study costs decrease. To explore this discrepancy further, a separate mean TTD was computed for students reporting different primary sources of support (Table 3.1~. In40f the 11 fieldsin 1986,andin9fieldsin 1987,fellowship recipients took less time to complete the degree than RAs. Likewise, in seven fields in both 1986 and 1987, fellows took less time to complete the doctorate than TAs. In nine fields in 1986 and 1987, students with research assistantships as their major source of support took less time to complete their doctorate than those with teaching assistantships. In all fields, students who used their own earnings as their primary source of income had substantially longer 'l-1US. For the 11 fields combined, fellows took less time to complete the doctorate than did TAs and those who used their own earnings to pay for school. While the type of primary support mechanism does appear to affect TTD, this variable is not available for the 1967-1986 period and cannot be tested by modeling. However, models developed in Chapters 5 and 6 that assess the impact of any support from a given source reveal that financial aid has no consistent effect on TTD. Effects on the Components of TTD As noted earlier, the three components of 'l-lD are time spent prior to graduate entrance (TPGE), registered time to the doctorate (RTD), and time not enrolled in the university (TNEU). In general, financial aid will reduce both TPGE and TNEU, but the effect of an increase in financial aid on RTD cannot be predicted with assurance, since it depends on the amount of foregone income replaced, the conditions under which aid is granted, and the form of aid received. Still, the expectation is that fellowships and dissertation-related research assistantships are more likely to lower RTD than nondoctorate-related research 39

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Go ~ - to To ox o v, -g ;^ - a, o - c) I) o .~ at; e - - A, b o ~ ~ - ~o Go - ~ 3 ~ - V TIC . or U' 1 So U Go 04 ~ .5 ~ U' a ~ at: I_-,lo,to ~Go ~or~4 o Us ~So ~ret ........... ~Cal ~Cal ~ ~_4 ~I_ I_ ~Go .- ~o I_~ ~Go ~ ~GoenO ~CalOCal ......... ~Cal ~Cal~ r ~0 ~ooO ~0 0r ~ooc~-O ....... ..... 00 ~o~ooo ~oo ~o ~c~ c ~r ~o ~0 oo0oo ~_ ~Oc~ ...... ..... Oo~ooooooor~o ~oo0 ~0 ~4 '_ ~o ~0r ~oo ~o ~ - ~ooooo ~O ...... ...- ~or ~oo ~oo ooOoo ~O ~_ r~0 ~oo\0c~O c~o ~c ~ooc~ ....... .....- ~o ~_ a, o ~0 ._ ~ ~ 0 - o - o oo .~ ._ oo _' ._ v~ oo ~0 ~O ~o c ~O ~o ~d. ~d oo ~r ~oo ~oo ~ oo ~oo ~oo oo ~oo oN oo oo o o .= =b o v, O ~C~doo ~o ~ .......~ oo ~oooS ~ooOooooooooo u, ~4 ~c) ~.5 ~ E ~E= ~a ~.a 40

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and teaching assistantships. Shortened TPGE occurs because financial aid makes it less costly for new graduates to pursue a graduate degree and increases the attractiveness of entering graduate school soon after completing an undergraduate degree.l Fellowships, which offer income without requiring a work commitment, are more likely to reduce TPGE than other forms of aid, particularly teaching assistantships and nondegree-related research assistantships. Whether one form of aid than another is more likely to affect TNEU will depend on its desirability relative to outside employment. For example, some students may prefer outside employment to teaching undergraduates. Market Forces and Completion Times The financial and other returns that students expect from completing a doctoral program can affect both their willingness to stay in school and 'low. The monetary incentive for earning a doctorate depends both on the absolute amount of the earnings expected and on the probability of employment. The returns from a given earnings stream and set of unemployment rates may be valued differently by students, depending on the importance they place on immediate versus future income and on their attitudes toward risk. Berger (1988) suggests that a single present-value measure can be used to incorporate expected returns into a model of student choice, but the analysis below assumes students consider expected earnings and the probability of unemployment separately. Effects of Changes in Relative Salaries Viewed from an opportunity-cost perspective, when starting salaries of new doctorates rise, income foregone by students while in graduate school increases. Increasing salaries increase the incentive for students to devote more time to completing doctorate and dissertation-related work, thus shortening TTD. The effect of salary on TTD may be partly offset, however, for Ph.D. candidates who get jobs before they finish their dissertation and are therefore likely to take longer to finish the doctorate. An increase in the salary ratio of already employed doctorates to new or recent doctorates can mean different things. If postdoctoral experience is rewarded 10 The effect is two-fold. The student foregoes less income to attend graduate school and also has immediate access to a source of financial support. The latter is important for those who do not wish to borrow to finance their education and to those with a strong preference for current income. 41

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such that salaries of experienced engineers are rising more rapidly than those of new entrants, for example, students have an incentive to complete their studies quickly. But if the increased salary ratio is the result of a poor market for new graduates, the signal is negative. Changes in relative salaries also affect the three components of AND: RTD: When salaries for new doctorates rise, graduate students will generally find it worthwhile to shorten RTD by spending more time in study and dissertation-related activities. However, departmentally defined constraints may limit the amount by which students can reduce RTD. TP(;E: When the doctorate salary increases, TPGE is expected to shorten because the opportunity cost to the student of waiting to obtain the doctorate diminishes. INEU: TNEU is likely to fall when the starting salary of new doctorates rises relative to that of nondoctorates and when the salary of a doctorate with work experience rises relative to that of a new doctorate. A real rise in the starting salaries of doctorates will cause a decline in TNEU if the salary of a nondoctorate remains unchanged. Effects of Employment Opportunities - Employment opportunities for new and recent doctorates are sometimes more visible and have greater impact on students than do relative salaries. Moreover, university placement offices are more likely to track the percentage of a graduating class with jobs than to compute the mean salaries of doctorates entering particular fields. The unemployment rate of new doctorates is an indicator of labor-market conditions and can be used in calculating future return for completing a doctoral program. When employment opportunities increase for new and recent Ph.D.s, the opportunity costs increase to those remaining in graduate school. This creates an incentive for those working toward the doctorate to substitute degree- related work for leisure activity or outside employment, resulting in lower TTD. Conversely, when the opportunity cost of remaining in school falls, I-I D for some students rises. The unemployment rates for new doctorates and for those without doctorates affect TTD in opposite directions. A rising unemployment rate for nondoctorates relative to the rate for doctorates increases the cost of remaining in graduate school, at least for those who either hold or plan to hold a non-university job, and will motivate students to finish the doctorate more rapidly. The percentage of students seeking employment or postdoctoral study will be used in lieu of unavailable unemployment data for new doctorates. 42

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Effects on the Components of TTD RTD: A rise in the unemployment rate for new doctorates leads to an increase in RTD and vice versa. An increase in unemployment among nondoctorates tends to lower RTD. TOP: A rise in unemployment for new doctorates increases TPGE, since it reduces apparent remans for earning a doctorate. But if the unemployment rate for nondoctorates rises relative to that for doctorates, TPGE will fall as the opportunity cost of attending graduate school is reduced. TNEU: A rise in the unemployment rate for new doctorates encourages students to find and retain jobs prior to receipt of the doctorate, even if doing so lengthens TTD and I-NEW. A rise in the nondoctorate unemployment rate, relative to the doctorate rate, reduces TNEU because it increases He benefits of obtaining the doctorate. The Variables Used To Develop the Model The primary source of the variables used in this study was the Doctorate Records File (DRE;) maintained by the Office of Scientific and Engineering Personnel (OS EP) of the National Research Council. The DRF is a data base of doctorate recipients from U.S. universities spanning the period 1920 to the present. DRF data on DID, RTD, TPGE, and TNEU for recent cohorts have been collected through the Survey of Earned Doctorates since 195S, although data on some of the variables became available more recently. OSEP also conducts the Survey of Doctorate Recipients (SDR), which provides biennial information on the employment status of scientific, engineering, and humanities doctorate holders.ll Information in the SDR data base is used to construct market-force variables. Except where otherwise noted, the variables are for U.S. citizens and permanent residents. Altogether, 41 separate variables, falling into the 5 vectors of the study family background, student attributes, tuition and financial aid, institutional environment, and market forces are used. 11 A more complete description of this data base may be found in Betty D. Maxfield and Mary Belisle, Science, Engineering, and Humanities Doctorates in the United States: 1983 Profile (Washington, D.C.: National Academy Press, 1985~. 43

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In addition to data from the DRF and SDR, information on federal funding of students and universities, student scores, earnings in alternative employment, and unemployment were obtained from a variety of sources, including Battelle Columbus Laboratories (BCL), the Bureau of Labor Statistics (BLS), College Placement Council (CPC), the Educational Testing Service (ETS), Northwestern University's Endicott Report (ER), the National Science Foundation (NSF), and a number of professional associations such as the American Institute of Physics (AIP) and the Higher Education Research Institute ~RI). Data on classification of schools by research type came from the 1987 Carnegie Classification of Institutions of Higher Education. Data for "top 20" rankings came from the National Research Council's 1981-82 Assessment of Research Doctorate Programs in the United States, using NSF data in the Computer-Aided Science Policy and Research System (CASPAR). 44