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s CHANGES IN TTD How well does the time-genes model discussed in Chapter 3 explain changes in ITD during the 1967-1986 period? To answer this question, two models are used, one based on a set of variables common to the 11 fields and a second based on a larger set of unique variables statistically significant at .05 confidence level. Although not exhaustive, the models nonetheless provide insights into what determines change in I-lL,. The goal of this inquiry is to answer two questions: (1) Is a unique variable or set of variables responsible for increases in AD in the 11 fields? and (2) Is there one model that explains the change in AD in all fields, or are the determinants of I1D specific to each field? Two different estimation models are employed to answer these questions. Common Variables Model Estimates derived from the common variables model are achieved in both linear and Big linear form using ordinary least-squares regression. Regression results are presented in Appendix Tables S and SA. A summary of the findings appears in Table 5.1. An F test indicates that all of the estimating equations are statistically significant except for agricultural sciences.l4 Differences do exist in the amount of variation in TTD explained by the equations, the standard error of the estimates, and the number of statistically significant independent variables. In six fields (chemistry, math, engineering, biosciences, psychology, and social sciences), the model explained 90 percent or more of the variation in I-11). The lowest standard errors of the estimate were found in chemistry and psychology. 14 Note that the linear time-trend model in Chapter 1 suggests the absence of a mend in this field. 69

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TABLE 5.1: Surnrnary of Common Linear Model Regression Results for UD, by Variable Variable Fields Statistically Correlation Significant (+/-) Female Social Sciences yes Age Chemistry yes Mathematics yes Biosciences yes Health Sciences yes Psychology yes Social Sciences yes Federal Support no + + + + + + Teaching Assistantship Psychology yes Research Assistantship Earth, Atmospheric, yes & Marine Sciences Psychology yes Baccalaureate from Foreign no Institution Baccalaureate from Category I Chemistry yes Research School Psychology yes Graduate Degree from no Category I Research School Number of Faculty no Salary Ratio: New Ph.D.s Chemistry yes to Ph.D.s 10 yrs after Degree Earth, Atmospheric, yes & Marine Sciences Unemployment Rate Chemistry yes of College-Educated Per-Capita Doctorates in United States Chemistry Engmeenng yes Biosciences yes Psychology yes yes 70

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Log Linear Equations A summary of the results from the log linear equations appears in Table 5.2. In the log linear equations, the adjusted R2s are above 90 percent in six fields, and the transformed standard errors are lower in every field than in the linear model. Further comparison of the linear and log linear estimates suggests the statistical significance of certain variables is sensitive to the model used. The log linear model does not appear to give the best estimates. Most important, a common set of variables is not responsible for changes in 1-~D in the 11 fields. Weaknesses of the Common Variables Model The common variables model has at least two important weaknesses. First, it constrains the variable set to be identical across fields even when some variables are not statistically significant. Second, many variables are included in the model, and the effects of some of the variables may be obscured by their correlation with others. Unique Variables Model In this model, the number of variables is vaned, and additional (but not exhaustive) variables beyond those used in the common variables model are introduced. Regression analysis is used to determine which variables in each field make a statistically significant contribution to Tow. Table 5.3 (pp. 74-75) summarizes the findings obtained using this approach by field. Summary of Findings A summary of the regression analyses is contained in Table 5.4 (p. 76~. The variable indicating female gender is significant and positive in one field in each of the three models. With the exception of age, no other variable is statistically significant in a majority of fields, although a majority of the variables are statistically significant in a limited number of fields. Many of the variables are not robust with respect to changes in the specification of the model. For example, the sign of the regression coefficient changed for the financial aid variables as the model specification changed. Finally, the analyses indicate individual field analysis is likely to be more productive than the simple dummy-variable approach employed by Abedi and 71

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TABLE 5.2: Summary of Common Log-Linear Model Regression Results for AND, by Variable Variable Fielders) Statistically Correlation Significant (+/-) Female Biosciences yes Age Federal Support Chemistry yes Physics tic Astronomy yes Mathematics yes Biosciences yes Health Sciences yes Psychology Social Sciences Teaching Assistantship Psychology Research Assistantship Baccalaureate from Foreign Institution Baccalaureate from Category I Chemistry Research School Graduate Degree from Category I Research School Number of Faculty Salary Ratio: New Ph.D.s to Ph.D.s 10 yrs after Degree Unemployment Rate of College-Educated Per-Capita Doctorates in United States yes yes no yes no no yes no Chemistry yes Biosciences yes no no Physics Bt Astronomy yes Earth, Atmospheric, yes tic Marine Sciences Biosciences yes 72

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Benkin (1987~. Each field has a set of unique variables that help explain much of the change in '1-1~. Limitations of the Analysis Because time-series analysis was used, a number of variables were highly collinear. But time and resource constraints did not permit an approach designed to isolate the unique effects of the variables. In addition, aggregation of the data to the cohort level may have obscured some of the variation within the cohorts that is, variables affecting student decisions at the individual level may not show up as important at the cohort level. Finally, there is a problem with interpreting the age variable. While age appears to be significant in a majority of fields, the analysis does not distinguish between physiological effects and cohort effects. The possibility cannot be ruled out that age is important because it serves as a proxy for other changes experienced by the cohort. Also, older people automatically have higher TPGE. Caution also must be taken when drawing conclusions from an analysis that relies solely on DID. TTD is a complex quantity, the sum of many separate decisions made at different points in time. Each decision point is of interest, and there is no guarantee that the same variables impact on decisionmaking at each point. This raises the possibility that a given variable may affect decisionmaking at more than one point in a student's career. Existing literature does not provide adequate understanding of this process, and studies of the- type described in Chapter 2 do not provide the insights necessary to identify the time at which individual variables impact on TTD. Additional work is needed on the lag structure implied by the model in Chapter 3 if a full understanding of the role of the independent variables is to be achieved. Despite these drawbacks, there is a need to model TTD if only because policymakers want to understand the supply of science and engineering personnel for the labor market. A better view of the impact of the independent variables likely will be obtained using the RTD model, since the decision points at which institutional and financial variables impact are easier to pinpoint. Finally, it should be noted that as an endpoint, AD may be less useful in answering some questions than RTD. If the goal is to determine whether financial aid causes students to remain in graduate school longer, RTD may provide a more accurate picture of student responsiveness. Likewise, if the goal is to examine the impact of institutional environment, RTD is the better variable. However, if the goal is to understand the role of market forces, Ills may be the better choice. 73

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TABLE 5.3: Summary of Unique Variables Model Regression Results for LID, Field Variables Correlation Comment ( ) Chemistry Age + The four variables together Dependents + accounted for 92 percent of Teaching Asst. + the variation in LID. A Baccalaureate from - one-year increase in age at Category I Research start of doctorate increased School TID by 3.5 years. A 10 percent rise in students with baccalaureates from Category I schools reduced 11D by almost five months. Physics and Age + The three variables together Astronomy Teaching Asst. + accounted for 90 percent of Percent Cohort + the variation in I1D. A Seeking one-year increase in age Employment boosted TTD by 2.13 years. Earth, Research Asst. Atmospheric, Baccalaureate from & Marine Category I Research Sciences School Percent Population with Doctorates Female + Mathematics/ Age + A one-year increase in age Computer Teaching Asst. + increased 11D by 4.5 years, Sciences Undergraduate Degree - suggesting the importance of in Same Field having doctoral candidates in this field entering graduate school at a young age. Engineering Age + A one-year increase in age Percent Population + lengthened 11D by 1.5 with Doctorates years. 74

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by Field Field Variables Agricultural Age Sciences Fed Support (decrease) + Tuition + Salary Ratio: New + Ph.D.s to Ph.D.s 10 yrs. after Degree Correlation Comment ( ) + A one-year increase in age increased TTD by 1.1 years. Biological Age + These three variables Sciences Graduate Degree from + accounted for 91 percent of Category I Research the variation in AND. A School one-year increase in age Percent Population - lengthened AD by 1.9 with Doctorates years. Health Age + A one-year jump in age Sciences Baccalaureate from - increased 1TD by two years. Foreign Institution Percent Population with Doctorates Psychology Marital Status Salary Ratio: New Ph.D.s to Ph.D.s 10 yrs. after Degree Fed Support Economics Age Baccalaureate from Category I Research School Salary Ratio: New Ph.D.s to Ph.D.s Social Sciences + 10 yrs. after Degree Percent Population with Doctorates Age Temp. U.S. Residents Receiving Ph.D.s Salary Ratio: New Ph.D.s to Ph.D.s 10 yrs. after Degree A one-year increase in age lengthened AD by nearly 11 months. The four variables together accounted for 84 percent of the change in T1'L). A one-year increase in age boosted 1TD by 1.3 years. 75

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TABLE 5.4: Number of Fields in Which Variable Has Statistically Significant Effect on TI D MODEL C OMM ON UNIQUE Linear I~og Linear Variable POS NEG POS NEG POS NEG WOMEN 1 0 1 0 1 0 AGE 6 0 7 0 9 0 SUPEEL) O O O O 0 2 SEPIA 0 1 0 1 3 0 SUPRA 1 1 0 ' O 0 1 FORBACC 0 0 0 0 O 1 BCARN1ST 0 2 0 1 1 3 PCARN1ST 0 0 0 0 1 0 FACULTY 0 0 0 2 0 0 SALRAT1 1 1 0 1 2 0 UNEMP4YR 0 1 0 1 0 0 PERPOP 0 4 0 3 0 0 MARRIED TEMP DEPEND SAMEFLD TUmON SDRSAL10 SEEK 1 0 lo O 1 0 0 3 1 0 1 1 1 NOTES: (1) "Pos" indicates a positive regression coefficient. "Neg" indicates a negative regression coefficient. (2) Variables below the dotted line were not entered in the common variables models. (3) For explanation of variables, see list of acronyms (Appendix B. pp. 175-177~. 76

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In short, whether 11D or RTD is the "better" dependent variable depends on which questions the researcher wishes to answer. Those studies that employ both 11D and RTD without distinguishing between the two may be ignoring the important differences between the two variables. What Car' Be Learned from the Findings? Despite the potential problems discussed above, this time-series analysis of I-lL) is encouraging in several respects. It suggests that 4. Total time to the doctorate can be modeled and such models explain much of the variation in the data in a time-series context. Age is the most consistent statistically significant variable, has a large impact on HID, and explains the largest amount of variation in the data. Variables from each of the five vectors act to determine HID. Moreover, the number of variables found to be statistically significant in this study is substantially greater than that found by Abedi and Benkin. Financial aid has an impact on HID, but not always in the intended direction. This interesting and provocative finding clearly warrants additional study in a cross-section or pooled tune-series cross-section analysis.iS At least some market variables affect HID. Since prior studies have not established this link, it opens a new avenue of inquiry for researchers interested in the determinants of time to the doctorate. It also supports the argument that market-place changes involving high- level personnel will occur as students adjust to market conditions. However, this analysis does not suggest that sufficiently large changes in ~-~L) can be achieved by changing financial aid policies or the institutional factors students are exposed to. It also provides little evidence that an infusion of additional resources would offset the increase in i-1 L,. 15 Aggregations of the type used here run the risk that some of the individual variation will be averaged out. Cross-section studies are almost certain to show a stronger relationship between federal support and 11D because the most promising students are the ones most likely to receive federal support and the most likely to complete degree requirements quickly. 77

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