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OCR for page 69

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.
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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
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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
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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.
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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.
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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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