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Modeling Faculty Replacement Demand at the
College Level in a Large Public University

presented by

Bruce Allen Montgomery

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MODELING FACULTY REPLACEMENT DEMAND
AT THE COLLEGE LEVEL IN A LARGE PUBLIC UNIVERSITY

BY

Bruce Allen Montgomery

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Educational Administration

1992

A ‘W A‘
V ,A w,
_ r, “'-

2 '/
7~ /

ABSTRACT

MODELING FACULTY REPLACEMENT DEMAND
AT THE COLLEGE LEVEL IN A LARGE PUBLIC UNIVERSITY

BY

Bruce Allen Montgomery

This study was designed.to analyze longitudinal changes in
faculty size and composition in three colleges at a large
public universityu The following characteristics were
selected for study in each college: total number of faculty,
average faculty age and salary, and the proportion of faculty
by academic rank, tenure status, racial/ethnic group, and
gender. It was found that the magnitude of change in faculty
characteristics between 1981 and 1991 varied greatly by
college. For example, the average age of faculty increased
in all three colleges between 1981 and 1991, but the increase

was statistically significant in only one of the colleges.

Time-dependent Markov chain models were developed on a
Macintosh® computer using the the Microsoft Excel 3.0©
software package to project the overall age, salary, academic
rank, and tenure status of faculty, five and ten years into
the future. The results of projections under three

hypothetical scenarios indicated that the characteristics of

the faculty would continue to change throughout the 19903,
the magnitude of these changes varying by college, time, and

scenario.

It was determined.that in order to maintain a stable size
faculty through the year 2001 under the assumption of the
continuance of historical transition rates, the number of
faculty hired per year would have to increase very slightly
above historical rates in two colleges, while the other
college could lower its historical hiring rates by over three
faculty per year and conceivably maintain a stable faculty
size. It was recommended that decision.makers continue to
monitor the impact of'a projected buildup of faculty in the

56 year-old and above age class in each college.

Dedicated to the memory of

Dr. Gary A. Simmons
1944-1991

~ Beloved friend, colleague, and mentor ~
Chair of this student's Masters Committees

Member of this student’s Doctoral Committee

iv

I express sincere appreciation to each member of my disserta-
tion and guidance committee: Dr. Eldon Nonnamaker (Chair),
Dr. Lou Hekhuis, Dr. Martha Hesse, Dr. Fred Ignatovich, and
Dr. James Lloyd. Each member made special contributions to

this project for which I am deeply indebted.

The data used in this study were made available through the
cooperation of the Office of the Provost, Michigan State
University and the special efforts of Dr. Robert Banks,
Assistant Provost and Assistant Vice President for Human
Resources and Dr. Martha Hesse, Assistant Director for Long
Range Planning, Office of Planning and Budgets. I am
especially grateful to Ms. Jeanne Kropp, Academic Personnel

Records Manager, who provided the data.

The following individuals made special contributions to this
work through thoughtful comments and the exchange of
information and ideas:

Dr. Richard Biedenweg, Stanford University

Dr. Michael Dooris, Pennsylvania State University

Dr. Judith Gill, WICHE

Ms. Ruth Kallio, The University of Michigan

Ms. Marilyn Knepp, The University of Michigan

Dr. Robert Lockhart, Michigan State University

Dr. Michael McGuire, Franklin and Marshall College
Dr. Steve Norrell, University of Alaska

Dr. Lou Anna Simon, Michigan State University

Ms. Veronica Tincher, University of Southern California

I am most appreciative of the support and encouragement from
Dr. Glenn Stevens, Executive Director of the Presidents

Council, State Universities of Michigan, and forihis consid-
eration and interest in helping out in so many different ways

in the workplace .

To my wife, Christie, and daughters, Rachel and Audrey, thank
you for the sacrifices that you made as I completed my

degree.

1992 Bruce Montgomery

vi

TABLE 0" CONTENTS

LIST OF TABLES
LIST OF FIGURES

CHAPTER 1. INTRODUCTION AND OVERVIEW OF THE PROBLEM
Overview of the problem
Anticipated faculty shortages
Faculty planning models
Objectives
Research questions
Methodology
Area 1. Change in faculty composition
Area 2. Model development and testing
Area 3. Model runs under different hiring and
separation scenarios
Limitations of the study
Definitions
Future suggested studies

CHAPTER 2. LITERATURE REVIEW
Chronological review of faculty planning models
Markov models
Approaches to model evaluation
Comparing projections of the model with
actual outcomes
Statistical tests of assumptions
Making assumptions as nearly correct as possible
Overview of the literature

CHAPTER 3. METHODOLOGY
Research design
Methodology by area
Area 1. Change in faculty composition
Area 2. Model development and testing
Expected and actual output
Area 3. Model runs under different hiring and
separation scenarios
Overview of the methodology

CHAPTER 4. RESULTS
Area 1
College of Business
College of Engineering
College of Natural Science

vii

84
84
9O
95

Area 2
College
College
College

Area 3
College
College
College

of Business
of Engineering
of Natural Science

of Business
of Engineering
of Natural Science

Stabilizing faculty size over time
Comparison of model output and models
Overview of results

CHAPTER.5. SUMMARY.AND DISCUSSION
Project overview
Summary and discussion of results

Area 1
Area 2
Area 3

Differences between scenarios
Stabilizing faculty size over time
Precautions

List of References

viii

101
103
107
109
112
113
117
121
125
127
129

132
132
137
137
142
143
150
151
152

154

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

2-1.

4-1.

4-2.

4-3.

4+4.

4-5.

4’6.

4-7.

4-8.

4-9.

LIST OF TABLES

Faculty flow'models by author, purpose,
analytical process, and evaluation
effort, since 1969.

Observed faculty frequencies in the
College of Business by academic rank and
tenure status, 1981 and 1991.

Observed faculty frequencies in the
College of Business by racial/ethnic
group and gender, 1981 and 1991.

Observed faculty frequencies in the
College of Engineering by rank and tenure
status, 1981 and 1991.

Observed faculty frequencies in the
College of Engineering by racial/ethnic
group and.gender, 1981 and 1991.

Observed faculty frequencies in the
College of Natural Science by rank and
tenure status, 1981 and 1991.

Observed faculty frequencies in the
College of Natural Science by racial/
ethnic group and gender, 1981 and 1991.

Projected and observed number of faculty
per state in the College of Business,
1991.

Projected.and.observed.number of faculty
per state in the College of Engineering,
1991.

Projected and observed number of faculty
per state in the College of Business,
1991.

ix

45

88

89

93

95

99

101

107

109

111

Table

Table

Table

Table

Table

Table

Table

Table

4-11.

4-12.

4-13.

4.14.

4-15.

Faculty'distributions projected for 1996
and.2001 under three scenarios, College
of Business.

Projected.age, salary, tenure, and.rank
characteristics of faculty in the College
of Business, 1996 and 2001.

Faculty'distributions projected for 1996
and.2001 under three scenarios, College
of Engineering.

Projected.age, salary, tenure, and.rank
characteristics of faculty in the College
of'Engineering, 1996 and 2001.

Faculty'distributions projected for 1996
and.2001 under three scenarios, College
of Natural Science.

Projected age, salary, tenure, and rank
characteristics of faculty in the College
of Natural Science, 1996 and 2001.

Historical hiring rates and projected
hiring rates (number of faculty per year)
to maintain a stable faculty size under
Scenario 1 between the years 1991 and
2001 by college.

Projected.faculty distributions in the
year 2001 under Scenario 1 using models
from each College with data from the
College and.the other two Colleges.

114

115

117

119

121

123

126

129

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

4-3.

LIST OF FIGURES

Transition matrix for faculty in LS&A,
after Johnson and Hinman (1975) and
Won (1976)

Career ladder flow chart, after
Feldt (1986)

Age class distribution of all faculty in
the College of Business, 1981 and 1991

Salary class distribution of all faculty
in the College of Business, 1981 and
1991

Age class distribution of all faculty in
the College of Engineering, 1981 and
1991

Salary class distribution of all faculty
in the College of Engineering, 1981 and
1991

Age class distribution of all faculty in
the College of Natural Science, 1981 and
1991

Salary class distribution of all faculty
in the College of Natural Science, 1981
and 1991

Transition matrix for faculty in the
College of Business .

Transition.matrix for faculty in the
College of Engineering.

Transition.matrix for faculty in the
College of Natural Science.

Age class distribution of faculty in the
College of Business, 1981, 1991, and 2001
projection -- Scenario 1.

xi

32

48

85

87

91

92

96

97

105

108

110

145

Fig. 5-2.

Fig. 5-3.

Age class distribution of faculty in the
College of Engineering, 1981, 1991, and
2001 projection -- Scenario 1.

Age class distribution of faculty in the

College of Natural Science, 1981, 1991,
and 2001 projection -- Scenario 1.

xii

145

146

CEAPTERI

INTRODUCTION AND OVERVIEW OF THE PROBLEM

Recent studies suggest that the number of faculty members in
the current cohort will decrease dramatically during the
19903 and that it will be increasingly difficult to find
candidates to replace them (Association of American
Universities, 1990, Atkinson, 1990, Bowen and Schuster, 1985,
1986, El-Khawas, 1989, 1990, Gamson, et. a1, 1990) . These
shortages are related to an increasing number of faculty who
are anticipated to leave higher education through resignation
or retirement and a decreasing number of candidates overall,
but particularly in high demand academic fields. El-Khawas
(1989) points out that it is unclear whether these trends
will cause widespread and severe dislocation in academe.

Yet, the potential impact of faculty shortages on individual
institutional programs has forced many colleges and

universities to do more long-term planning (Mooney, 1989) .

Much of the research on the academic labor market has focused
on the nation-wide supply and demand of faculty, adding
little conclusive evidence for policy-making at the college
level (Blum, 1991). In fact, WICHE's (1991) annotated
bibliography of the literature on faculty supply and demand

1

2
identified nearly 83 articles, books, and reports, none of
which had addressed the issue of faculty supply and demand at
the departmental or college level. A major purpose of this
study was to develop a technique to estimate the impact of
faculty hiring, promotion, and separation scenarios on future
faculty age class structures, tenure ratios, appointment

distributions, and salary levels at the college level.

Overview of the problem

Wages

The American Council on Education recently reported that many
colleges and universities in the United States are unable to
fill full-time faculty positions in computer science,
business, mathematics and the health professions (El-Khawas,
1989) . This shortage is expected to worsen in these four
areas and to widen and include a range of academic
disciplines over the next ten years. Nearly two-thirds of
all colleges and universities are reporting that it takes
longer to find qualified persons for full-time faculty
positions and that it is more difficult to get top applicants
to accept faculty positions offered to them (El-Khawas,

1990) . This proportion has doubled in only two years.

Such shifts in the academic labor market are products of what
Cartter (1976) calls replacement demand and enrollment
demand. Replacement demand includes those factors related to

faculty retirement and the net migration into and out of

3
academic careers. IEnrollment demand pertains to the overall
impact of college enrollments and student-faculty ratios on

the faculty labor market.

Much of the anticipated attrition will result from.dramatic
changes in replacement demand as a natural consequence of the
aging of the faculty, many of whom were hired in the 19503
and 19603 in response to burgeoning enrollments. Today, more
than one-third of the faculty in the nation are over age 50
(Mooney, 1989) and the rate of faculty retirement is
projected to increase from.approximately 20 percent to 30
percent between the years 1987 and 2000 (Lozier and Dooris,
1988-89). At Michigan State University, for example, 40
percent of all faculty members and.50 percent of faculty
members in the humanities will be 65 years old.by the year
2000 (Mooney, 1989).

Bowen and.Schuster (1985, 1986) suggest that deteriorating
conditions on campuses are also making it increasingly
difficult to attract and retain faculty due to:

0 real and perceived decline in compensation,

- disproportionately high salaries for new faculty in
high demand academic disciplines creating a condition
of salary compression,

- deteriorating work conditions and generally low morale
as a result of'tight budgets and shifting

institutional priorities and reward.3ystems, and

4
- jpressure on the junior faculty to publish, on
mid-careerists to keep up, and on senior faculty to

adjust to the surge toward research.

Bowen and Schuster (1985, 1986) and Schuster and Bowen (1985)
estimate that the average annual turnover rate of faculty
will increase from 4 percent in recent years to 6 to 8
percent in the future largely through early retirement and
transfer to other industries and professions outside of
academe. They find that an increasing number of the most
capable college students are opting for employment outside of
academe. In 1985, 43 percent of all Ph.D.s were working
outside of higher education. Of the students who graduated
with Ph.D.s in 1987, 50 percent were employed outside of
academe; with rates of 70 percent for Ph.D.s in engineering
and 50 percent for Ph.D.s in the physical sciences

(Association of American Universities, 1990).

The pool of Ph.D.s has remained relatively stable during the
19803. However, the number of doctorates earned.by U.S.
citizens has dropped from 25,008 in 1977 to 22,396 in 1987
(Association.offimmerican'Universities, 1990). .Additionally,
non-Asian minorities continue to be underrepresented in
graduate programs. Black males received 684 Ph.D.s in 1977
but only 317 Ph.D.s in 1987 (Association of American
Universities, 1990). Although blacks make up 12 percent of

the population in the 0.3., only 3.4 percent of the

5
doctorates awarded.to U.S. citizens in 1987 were awarded to
blacks. Likewise, Hispanics make up 6.5 percent of the
population, yet received just 2.8 percent of the doctorates
awarded to 0.5. citizens in 1987 (Association of American
Universities, 1990) . A disproportionate number of doctorates
awarded to minorities were in the field of education. 'Very
few doctorates were awarded to minorities or women in the
physical sciences or engineering (Association of American

Universities, 1990).

In addition to anticipated changes in replacement demand,
many researchers are expecting a concurrent increase in the
enrollment demand for faculty. Some of the increased demand
for faculty is related to an expected resurgence in
enrollments in the late 19903 in response to an increasing
pool of high school graduates (Hexter, 1990) . And colleges
and universities continue to experience an increase in
enrollment levels of students over age 25 and improved
retention of enrolled students (El-Khawas, 1989) . Likewise,
in response to financial needs, more students are taking
longer to complete their degrees, adding to the annual

headcount totals (Dickey, et al., 1989) .

Until recently, college and university administrators were
concerned about a surplus of faculty (Mooney, 1989) . In 1994,
the federal mandatory retirement age for faculty will no

longer exist and some administrators in higher education

6
anticipate that many faculty will not retire until they are
well into their 703 and 803. In Michigan, Public Act 11 of
1991 prohibits requiring "an employee of an institution of
higher education who is serving under a contract of unlimited
tenure, or similar arrangement providing for unlimited tenure
to retire from employment on the basis of the employee's age"

(Sec 202, 1, d), effective May, 1, 1991.

Partly in an attempt to reduce the proportion of older,
tenured faculty» 51 public colleges and universities surveyed
by Chronister and Trainer (1985) had established 62 early,
partial, and.pha3ed retirement programs for faculty, with 40
programs implemented after 1979. Yet, Lozier and.Dooris
(1988-89) reported.that fewer than 5 percent of faculty have
currently deferred retirement until after age 70 at
institutions with no mandatory retirement. They suggest that
the capacity of institutions to replace the large number of
faculty who will retire before the year 2000 may be of
greater concern. On the other hand, in a more recent report,
Lozier and Dooris (1991) found that nearly 20 percent of 400
surveyed faculty would have worked.past age 70 if mandatory

retirement had not been a factor.

Bowen and Schuster (1985, 1986) forecast that 400,000 to
500,000 new faculty appointments will be needed over the next
25 years, an average of 20,000 appointments per year. By the

early 20003, the.Association of American Universities (1990)

7
projects an annual shortage of 7,500 natural science and
engineering Ph.D.s in institutions of higher education. The
Association predicts that only seven candidates will be
available for every ten positions in the humanities and
social sciences between 1997 and 2002. Atkinson (1990)
projects an annual shortage of 9,600 Ph.D.s in the natural

sciences and engineering from 1995 to 2020 for all sectors.

Some colleges and universities are beginning to prepare for
anticipated faculty shortages in hopes of minimizing negative
consequences to institutional programs (Mooney, 1989) . The
Association of American Universities (1990) has suggested
several alternatives, aimed primarily at the federal
government, to increase the number of prospective faculty
members. The American Association of State Colleges and
Universities (1990) has developed a program which coordinates
and ensures the return of a doctoral student to the faculty

of an institution which pays for‘that student's education.

Lozier and Dooris (1988-89) listed six approaches to minimize
faculty shortages, one of which was to monitor faculty flow
systematically. Monitoring selected trends of interest to an
organization is the first stage in long-range planning
(Morrison,1987 and Morrison, et al., 1984) . "The dynamic of
the monitoring process is one in which information is used to
compare, confirm, or question expectations about human

service problems and programs" (McClintock, 1987) .

Eacnlthlannimndels

As described below, faculty planning models provide a means
of describing a portion of an institution's future
organizational structure under hypothetical scenarios --
scenarios which can be derived from environmental and
institutional scanning and analysis. Hopkins and Massy
(1981) discuss several reasons why modeling university
personnel systems are important. First, they note that the
salary costs for faculty and staff dominate the expense side
of the university budget making employment levels of
university personnel ”primary planning variables. " Planners
must also consider the impact of employment levels on
academic vitality including the maintenance of an adequate

flow of new faculty into the institution's academic programs.

Hopkins and Massy (1981) also (point out the usefulness of
faculty planning models with regard to testing the effects of
staff size and hiring mix on the numbers of women and members
of ethnic minority group members. Affirmative action goals
can be set within "the limits of feasibility rather than

being the products of merely wishful thinking.”

Although the recent literature on faculty supply and demand
issues has concentrated on national, regional, and
disciplinary trends (WICHE, 1991), much of the literature in
the 19703 was oriented toward the development of models which

could be used to forecast the number of faculty over time in

a single institution.

Faculty flow'models were first developed in the early 19703
when shifts in enrollment patterns toward professional-
oriented curricula resulted in a surplus of faculty in some
areas and shortages in others (Bleau, 1982). The Stanford
faculty flow model developed.by Hopkins (1974) and since
refined.by Bloomfield (1977), Bleau (1982), and.Feldt (1986)
used Markov chains with stationary transition probabilities
to project future faculty staffing under different planning
strategies and.policies. Planning models are described in

detail in Chapter 2.

Objectives

The principal objectives of this study were: (1) to review
the changes in composition of the faculty in three colleges
of a large public university during the 19803 in terms of
faculty size, age, gender, ethnic background, tenure
distribution, and rank, (2) to develop a model that could be
used on Macintosh computers to project the number of faculty
by age class, tenure status, academic rank, and salary level
in academic units with 100 or more faculty, (3) to conduct
several case studies projecting faculty distributions in
five- year time periods under different hiring, promotion,
and separation scenarios, and (4) to analyze the policy
implications of the different case-study scenarios on faculty

size, age class distribution, and budgets. The model would

10
be validated by comparing observed and theoretical
distributions for faculty cohorts in the selected academic

units.

Research questions

This study was designed to answer questions in three areas:
1. Was the composition of the faculty in terms of average
age, real salary, racial-ethnic composition, gender, tenure
ratios, or appointment levels significantly different in 1991
from faculty composition in 1981? Was this change consistent
between the three sampled colleges? Or did the average age,
racial composition, gender, tenure ratios, or appointment
levels of the faculty differ significantly between the three

colleges?

2. Can an acceptable model be developed on a Macintosh
computer using a popular spreadsheet software program to
project the faculty distributions in colleges with 100 to 400
faculty members? The measure of acceptance will be the
congruence of actual distributions with theoretical

distributions as projected with the model.

3. Assuming that a reasonably accurate model was deveIOped,
the third question area investigated what faculty distribu-
tions by age class, tenure, academic rank, and salary level
could be anticipated in 3 colleges under different hiring and

separation scenarios? Several specific policy scenarios were

11
investigated by changing different model components. For
example, what would.be the budgetary consequences if no new
faculty members were hired over a given period of time? How
would the ages and ranks of a faculty be distributed in five
or ten years if historical transition rates were to continue?
Are the distributions significantly different from other
distributions within and between colleges?'.Answers to these
questions helped indicate the level of impact that variables
related to hiring and separation rates might have on the
number and.distribution of faculty members by age, tenure

status, salary level, and academic rank.

Methodology
The methodology for each of the three areas of interest is
described below. More details on the methods used to complete

this study are presented in Chapter 3.

NW

The purpose of this portion of the study was to analyze the
differences in the composition of the faculty over a ten-year
time frame. The target population included faculty in three
colleges at Michigan State University (MSU) -- the College of
Business, the College of Engineering, and the College of
Natural Science. The colleges were selected because of their
relatively large sizes and their representation of
disciplines projected to undergo increasingly severe faculty

shortages during the 19903 across the nation.

12
The following descriptive statistics were determined for two
variables, age and salary, within each college for the years
1981 and 1991: the population size, mean, median, mode,
range, standard deviation, and the frequency distribution.
Statistics for the nominal variables of race/ethnicity
(Asian, black, or other), tenure status (tenure track or
tenure), and academic rank (assistant professor, associate
professor, or professor) included population size and range
and the proportion as the mean, standard error and sampling

distribution of each proportion.

The first null hypothesis stated that there was no difference
in mean age between 1981 and 1991 or mean salary (adjusted

for inflation) between 1981 and 1991. The student t-test at
the 0.05 a-level was used to test for statistical difference

between the means.

The second null hypothesis stated that a proportion of the
population, 1:, possessing a particular characteristic -
proportion Asian, proportion black, proportion tenured, and
proportion at the rank of professor - was equal to a value K
that lies between 0 and 1. Differences between the means for
the nominal variables of race/ethnicity, tenure status, and
academic rank as proportions of total faculty in 1981 and
1991, were tested for significance with the chi-square
goodness-of-fit test. Results of the descriptive analyses

were presented in tabular and graphical formats.

13

MW.

Markov chains with stationary transition probabilities were

used to develop time-dependent models for tracing faculty

flows in each college. The general law of motion for the

Markov model was defined by Hopkins and Massy as:

Nju: + 1) = ijjNfit) + fj(t + 1) j = 1, 2, ..., 14.
where, Nj(t + 1) is the number of faculty in state j at
time t + 1; pij is the probability of an individual
currently in state 1' moving to j in the next time
period; and fj represents the number of new faculty

moving into a state j from outside the college.

A 17-state model, designed after Hopkins and Massy (1981) and

Bleau (1981) , provided projections of tenure status and

academic rank and corresponding appointment rates over time,

by age.

HHHHHHHt—I
qmmcwmpommqmmbwwp

Tenure track-Assistant Professor-Age 26-35
Tenure track-Assistant Professor-Age 36-45
Tenure track-Assistant Professor-Age 46-55
Tenure-Associate Professor-Age 26-35
Tenure-Professor-Age26-35
Tenure-Associate Professor-Age 36-45
Tenure-Professor-Age 36-45
Tenure-Associate Professor-Age 46-55
Tenure-Professor-Age 4 6-55
Tenure-Associate Professor-Age 56-65
Tenure-Professor-Age 56-65
Tenure-Associate Professor-Age 66-75
Tenure-Professor-Age 66-75

Resignation

Termination

Death

Retirement

14
Transition probabilities were averaged over ten years for the
MSU study, resulting in a 13 x 17 transition matrix, M. The

resulting transition matrix was shown in Chapter 4.

Ag(t) was a 17—component row vector, where each component was
the faculty level by state at the start of year t. The
17-component row vector, fj(t + 1), denoted the number of new
appointments made to each respective component in year t + 1,
where states 14-17 were valued at 0 since no new hires were

made directly to exit states.

Like the Hopkins and Massy and Bleau studies, the MSU
transition fractions were obtained from actual movements of
each faculty member who served in each of the selected
colleges. A standardized array table was set up to track
each faculty member as he or she moved within a college.
Differences between actual and projected number of faculty by
state were tested for significance by comparing 1981 faculty
levels projected.over 10 years with the actual faculty levels

using'chi-squareigoodness-of-fit tests.

ARLLJstmendemuferentmirinLaanenaratinn
scenarios
The following model runs were made with the actual 1991
faculty distributions to the years 1996 and 2001:

1. Continue historic promotion patterns, distribution and

rate of new hires, and separation rates. This model

15
run would assume no major policy changes.
2. Continue historic promotion patterns and separation
rates but no new hires between 1992 and 1996.
3. Continue historic promotion patterns and distribution
rate of new hires but lower retirement rates by 10
percent for 56 to 65 year—old faculty during each year

of the model run.

Scenario 1 was selected to provide a baseline of faculty
distributions to compare output from the other two model
runs. It also is a likely scenario particularly if one
subscribes to the paradigm that change is relatively slow and
often undetectable in institutions of higher education (e.g.,
student test scores on entrance exams, faculty tenure ratios,

etc.).

Scenario 2 was selected due to the current fiscal crisis in
the state of Michigan and the potential for cuts or at least
very small increases to state appropriations for higher
education institutions during the mid and early 19903. (Also,
reallocations and budget cuts within institutions have
recurred throughout the 19803, leaving most institutions with
limited flexibility for future cost-saving measures other

than to continue not to fill vacant faculty positions.

Evidence for Scenario 3 was provided by Lozier and Dooris

(1991) who found that 20 percent of 400 surveyed faculty

16
members would have continued employment past age 70 if
mandatory retirement had not been in effect. Although there
are a number of environmental and personal reasons involved
in a decision to retire, it is plausible that the abolishment
of mandatory retirement for faculty members in Michigan
institutions of higher education in 1991 might influence the
retirement decision of some faculty. An arbitrary rate of 10
percent was selected to fit somewhere between the 5 percent
who actually deferred retirement after age 70 at institutions
with no mandatory retirement and the 20 percent who in
response to a hypothetical question Lozier and Dooris (1991)
would have deferred retirement past age 70 if mandatory

retirement had not been a factor.

The following results from model runs were reported in
Chapter 4 for each year, 1996 and 2001, and each scenario:
the number of faculty in states 1-13, total number of
faculty, average age of all faculty, average adjusted salary,
total salary, number and proportion tenured, and number and

proportion by academic rank.

Limitations of the study

This study was designed to provide insight into the potential
effects of various hiring, promotion and separation decisions
on the composition of tenure system faculty. It was not
intended to supersede current policies designed to ensure

equal opportunity for employment, promotion and advancement.

17
Academic personnel policies are the result of years of
academic discourse and experience and are typically adopted
by governing boards for the protection of personnel and the
institution. Models such as the one developed and used in
this paper are meant to point out the long-term importance
and potential consequences of personnel policies not to
displace them. As such, this study and its results should be
limited to studying institutional personnel systems not to

displace them .

The generalizability of the results of this study is limited
to each academic unit included in the study and.not to other
academic units within Michigan State University or other
institutions. The subjects for this case study were from a
finite population and were not randomly selected” .As such,
the policy implications apply to three sets of faculty only.
The faculty distributions in the three academic units may not
be representative of distributions in the larger cohort of
faculty at Michigan State University or in other similar

units at other universities.

For example, MSU is a public institution, funded in part with
state appropriations, with over 1,850 tenure track faculty
members and over 43,000 headcount students (Fall, 1991) . The
faculty are not unionized and all faculty appointments
involve the University making a continuing basic employment

commitment to academic year appointments only. The award of

18
tenure is approved on an individual basis by the Board of
Trustees following successive review'by the Dean and the
Provost and approval and final recommendation to the Board by

the President.

The College of Natural Science represents a large academic
unit with over 400 faculty members, many of whom have joint
appointments in other departments or colleges. The College
of Business and.the College of Engineering are smaller
academic units with between 100 and 150 faculty members, and
not as many joint appointments as would be found in Natural
Science. Thus, each sample in this study is identical to the
population and its inferences are specific to that

population.

Third, the faculty cohorts include only tenure system
facultyu Part-time faculty, instructors and lecturers, and
graduate teaching assistants are assuming greater roles and
becoming more prevalent in some colleges and.nniversities.
Faculty and others not in the tenure stream may have
significant.policy implications and.subsequent impact on
future hiring, promotion, and separation rates which are not

accounted for in this study.

Due to the nature of the tenure system, faculty personnel
distributions generally remain quite stable over time» Once

promoted.to tenure, a very small proportion of the faculty

19
separate from the university in any given year. The
opportunity costs are generally too high.for most tenured
faculty members to relocate and few if any tenured faculty
are terminated" Therefore, even though.policy changes may
occur which would effect faculty hiring, promotion or
separation rates, it may take years for such.policies to have
noticeable, let alone significant, impact on faculty
distributions. For example, Hopkins (1974) and others have
shown through their models that in order to impact the
faculty distribution in terms of affirmative action goals, a
tremendous increase in the hiring rates for minority and
female faculty members would be required over a significant
period of time. The impact of hiring just one or two
additional minority or female faculty members each year was

found to be numerically negligible.

The model is deterministic and assumes that mean transition
probabilities provide perfect information. In fact, the
transition probabilities averaged.over a given time frame
merely'provide estimates of historical transition rates which
are subject to errors in reporting and vagaries of the
faculty cohort over a given time frame. .As averages, these
values may not capture important policy decisions in a given
year and tend.to mask significant changes in a given year as
a result of averaging. Standard errors about each mean
transition probability were not used to calculate confidence

intervals for the projected number of faulty per state

20
because it was assumed that the variation in transition

probabilities over time was not significant.

Another limitation of this study was that the model was based
on the assumption that faculty transition rates will continue
to remain relatively stable over time when in fact they may
not. However, the importance of this limitation may be
negligible if one subscribes to the paradigm of resiliency in
faculty flow over time and since the model allows for
altering transition rates to account for hypothetical

variations in faculty flows.

Lastly, this study examined only replacement demand and did
not examine enrollment demand. Potential changes in the
number of students in a given college would also influence
the number of faculty members in a given college but
estimates of future student enrollment were not included in
this study directly. Albeit, the policy changes related to
faculty hiring and separation rates might reflect changes
related to increased or decreased student enrollment in a
college. However, the different rates in this study were
selected to represent hypothetical policy changes consistent
across all three colleges and do not necessarily reflect real
or potential changes in enrollment demand. As such,
enrollment demand in this study was assumed to be constant
over the given time frame but could have been included as a

basis for altering hiring and separation rates.

21
Definitions
Several terms used in this dissertation are defined below.

W11]: - the rank to which a faculty member is
assigned initially at the date of appointment or through
promotion, including assistant professor, associate
professor, or professor.

Academiunir - a subdivision of the university commonly
organized around academic disciplines. (At MSU, academic
units include colleges, schools, and departments in a college
or colleges) .

- a non-tenured rank in the MSU tenure
system in which the faculty member serves for a probationary
period of four years and may be reappointed for an additional
probationary period of three years. If the assistant
professor is appointed beyond the two probationary periods,
tenure is granted. If at any time during the probationary
periods an assistant professor is appointed to the rank of
associate professor, tenure is granted.

Associaterrofessgr - an academic rank in the MSU tenure
system to which a faculty member may be appointed with or
without tenure or to which a faculty member may be promoted
from the rank of assistant professor at which time tenure is
granted automatically .

millage - a primary academic unit of the University which
contains smaller sub-units called departments. At MSU,
faculty members may have joint appointments in more than one
primary academic unit.

WW - All faculty in the tenure system at MSU
are appointed on either an academic year basis (a nine-month

assignment of duties and responsibilities) or an annual year
basis, both considered full-time for the purposes of this
study.

- historical or future salary levels which are
not adjusted for inflation.

Professor - the highest academic rank in the MSU tenure
system for active faculty members, automatically granted
tenure from the date of appointment at that rank.

- historical or future salary levels which are
adjusted for inflation at a given rate or index.

Salary - Base salary of faculty over a 12 month period.
Salary in this study does not include fringe benefits or
other compensation.

22
Tenure - A policy commitment by the university to assure the

university faculty academic freedom and security and to
protect the best interests of the university.

Wag]; - Faculty members in the tenure system at the
rank of assistant professor or associate professor who have
not been granted tenure and are on probationary status.
W - Faculty members in the tenure system
at the rank of associate professor or professor who have been
granted tenure.

l'uture suggested studies

Several studies are suggested as a result of this
dissertation. For example, several improvements could be
made to the models developed in this study. It would be of
particular value to review more closely the sensitivity of
the model output to variations in the rate of change of
selected variables. Although faculty distributions are
relatively stable over time, it is highly likely that there
would be some deviations from the average historic transition
rates and hiring rates. The relative sensitivity of the

model could be determined by making small changes in

transition rates and comparing the resulting distributions.

After the models are further refined, it would be of interest
to broaden the analysis to all colleges within the MSU to get
a more complete survey of projected change in faculty
composition and further enlarge the analysis to other large
universities in the state or the region. No recent studies
have modeled faculty flow at individual institutions and no
studies have been conducted which would project faculty flow

in various disciplines for a specific set of universities.

23
Based upon the results of this study, the MSU model could be
used to analyze faculty flow in several key academic
disciplines in other large public universities across the
country. Such an analysis would require attention to the
inter-connectedness of faculty flow between the institutions,
including a closer look at replacement and enrollment

demands.

The statewide implications of potential faculty supply and
demand levels are unknown. Faculty shortages may have
important ramifications on the nature of public higher
education in Michigan and on the capacity of the institutions
to meet the educational and economic needs of the state and
its citizenry. An additional study is recommended to
evaluate the economic and social impact of projected faculty
flow on the public universities and the state of Michigan.
Future studies must also investigate how the use of part-time
faculty, adjunct faculty, faculty who partially separate from
the university but continue in some part-time function, and
graduate teaching assistants are affecting the composition of

full-time tenure or tenure-track faculty.

The capacity of the universities to anticipate and minimize
the impact of undesired faculty flow is related to a number
of variables. These variables are internal or external to the
university environment and are controllable to varying

degrees through policies and practices. For example, the

24
elimination of the mandatory retirement age for faculty
members is an example of an exogenous variable which is not
controllable by the universities. It may, however, have
important implications on faculty flow; On the other hand,
an incentive to encourage certain faculty to retire is an
example of an endogenous variable which would also have

important implications on faculty flow.

A third study is recommended to analyze the endogenous and
exogenous variables which.influence faculty flow and
determine the relative sensitivity of faculty flow to their
manipulation. Based on the results, a set of alternative
policies could be provided which would have varying effects
on faculty flow. The implications of the policies will be
analyzed within an array of economic, social, political, and

institutionalconsiderations.

Lastly, the current study did.not include models which.would
project the institution's progress in fulfilling goals
related.to affirmative action. One of the Hopkins (1974)
models addressed this issue and.would appear to be a useful
starting point for future model development regarding the
projections of the racial/ethnic and.gender composition of
the faculty and the impact of hypothetical policy scenarios

on this future composition.

CBAPTER.2

LITERATUREINIVIEH

Hopkins (1974) defined a faculty flow model as a "planning
tool used by decision makers to investigate the various
institutional practices that can, and do, influence the
number of faculty positions to be filled." Such models math-
ematically describe the relationships among variables
including demographics of institutional faculty, promotion
policy, retirement policy, and long-range staffing goals.
"Without a model, decision makers can only guess at how their
policies will affect academic staffing" due to the
complicated relationships among a large number of variables

(Mortimer, et al., 1985, p. 59) .

Faculty planning models have been used to examine the
potential effects of alternative policies in relation to
desired outcomes, the relative influence of variables on
faculty demographics, and the probable future makeup of the
faculty. Bleau (1982) found that many previous models were
used in reaction to the development of a surplus of faculty
in some areas and shortages in others. This imbalance had
resulted partially from shifts in enrollment patterns toward
professional-oriented curricula in the 19703 and early 19803.

25

26
Faculty planning models in colleges and universities were
offshoots of flow models in the industrial sector where they
had been used for long-term projections of personnel
movements within firms. Forbes (1971) and Bartholomew (1969)
were the first workers to use "manpower" flow models in a
true planning sense with the goal of having "the right number
of people in the right jobs at the right time" (Bartholomew

and Forbes, 1979, p. 1).

Chronological review of faculty planning models

A three-stage equilibrium model at the University of
California at Berkeley (Oliver, 1969) was one of the first
attempts at a university to model the flow of tenured and
tenure-track faculty and the effect of promotion policies on
the magnitude of the flows. Faced with quota restrictions on
faculty appointments, the model assumed a constant number of
faculty over time. Hopkins and Bienenstock (1975) refined
Oliver's (1969) model into a two-state equilibrium model to
analyze the long-term effects of policy changes on a faculty
of fixed size. Bleau (1982) judged both equilibrium models
to be "rudimentary" in that neither provided opportunities
for mathematically altering the faculty distribution over

time.

The equilibrium models gave way quickly to the more flexible
time-dependent Markov-chain model. The basis of the Markov-

chain model is a matrix where each row and column corresponds

27
to a current faculty state (e.g., tenure status,and age,
retirement, resignation or death) . The coefficients in the
matrix refer to the probabilities with which faculty members
will move to different states. Transition probabilities can
be adjusted from year to year as university policies or
external conditions change (Bloomfield, 1977) . The number of
members per state must be large enough to avoid violating a
primary assumption of Markov chain models, i.e., the
transition probabilities for a state remain constant over
time. As a time-dependent model, faculty movements can be
projected from year to year. This provides not only a
forecast of faculty distributions but a means for adjusting
the transition probabilities to reflect changing institu-
tional conditions, policies, or practices. The mathematical
properties of the Markov-chain model are reviewed in the next

section.

Stanford University took the lead in developing Markov-based
faculty planning models in higher education largely as a
reaction to financial problems and as a conduit to its stated
tradition of open and centralized planning (Hopkins and
Massey, 1981) . Hopkins' (1974) Markov-chain model was used to
vary policy parameters and, in effect, transition probabili-
ties to analyze the impact of differing promotion rates to
tenure, early retirement policies, affirmative action
policies, retrenchment, and tenure distributions on faculty

composition. The 1974 ”Stanford model" was not suitable for

28
a number of other institutions due to the assumptions that
only three ways exist to leave the institution (resignation,
retirement, or death), no mechanisms were provided for
including fixed-term or part-time appointments, and movement
to the tenure and associate professor state occurred simulta-
neously. However, the Stanford model has provided the
framework for development of virtually all faculty planning
models based on Markov processes. Biedenweg and Keenan
(1989) developed a commercial version of the Stanford faculty
planning for use with an IBM-compatible personal computer and

LOTUS 123 software.

Adapted from the Stanford model, the more comprehensive
Oregon State University (OSU) model (Bloomfield, 1977)
provided the flexibility to vary the entering tenure-track
rank, disassociate tenure from the rank of associate
professor, and allow for high and variable separation rates
even for tenured faculty. OSU first assembled an historical
profile of the institution's entire faculty for four years.
Faculty states were aggregated according to trends in
promotion and tenure decisions. Transition probabilities
were established for each of a possible 161 states with an
average of 34 faculty members per state. New faculty hires
were specified according to percent change per rank as
indicated by historical observations. This was deemed
justifiable at OSU since this rate had been consistent from

year to year. However, as the author noted, other rules may

29
be required when distributions of new hires to replace
departing faculty members of different ranks are not uniform,
or equally important, when the institution attempts to change

set distributions .

Twenty-year forecasts of the rank distribution and the tenure
distribution predicted "substantial stability" in faculty
ranks and the numbers of tenured and tenure-track faculty
during this period at OSU. A committed resources index based
on rank and tenure distributions was used to predict total
faculty size as derived from forecasted student enrollment.
With such "inherent properties of stability, " sensitivity
analysis of the model only showed that drastic changes in
staffing policies or transition trends would significantly

affect future distributions.

Limitations of this model included transition rates which did
not account for the changing financial status of the
university or the relative strength of the external academic
market. Administrative reactions to lower state funds might
require increased standards for tenure and promotion.
Consequently, a deteriorating academic market might permit a
university to hire new faculty members with significantly
better credentials, who would in the long run satisfy
stricter tenure and promotion criteria and bring about lower
rates of involuntary separation. Additionally, the distribu-

tion of temporary faculty members is greatly influenced by

30
enrollment patterns. As noted, such uncertainties emphasize
the value of studies which.estimate the "global sensitivity
of the comprehensive model over wide intervals containing

possible values of transition probabilities . "

An adaptation of Hopkins' (1974) Stanford faculty flow model
was developed by Johnson and.Hinman (1975) at the University
of’Michigan» ‘Won (1976) described the structure and

mechanics of the model, while Gross (1979) revised the model

and conducted.a follow-up study.

Johnson and Hinman (1975) used the Markov process model to
test the effects of several policies on the future age-class
and rank distributions of faculty in the University's largest
school, the School of Literature, Science, and.the Arts
(LS&A) through 1995 at five-year intervals beginning in 1975.
The Johnson-Hinman model used 18 states, the same number of
states used by Hopkins (1974). States number 1 through 7
were the tenure track states with state 1 representing the
first year of service through state 7 which represented the
7th year of service. States 8 through 15 were the tenured
states with state 8 occupied.by tenured faulty age 30-34,
proceeding in five year increments to state 15 where tenured
faculty were ages 65 to 69. New faculty could enter only at
states 1 and 8 to 15. No faculty member could jump more than
one state forward at a time, except to one of the terminal

states, 16tx>18, retirement, resignation, and death.

31
Other assumptions follow directly from the general list
reported in the following section on Markov process models.
For example, transition probabilities were considered
stationary. The probability of movement from one state to
another (e.g., state 1 to state 2) would be the same for any
year of the analysis. Additionally, the probability of
transition from one state to another is independent of the
faculty member's history before reaching the state. Thus,
the probability of a tenured instructor's resignation between
the ages of 40 and 44 (state 10) is the same whether he or
she entered the faulty at state 1 and.proceeded through each
state to state 10 or entered at state 1 but gained tenure
after only five years instead of seven and entered at state 9

(Won, 1976).

The resulting transition probabilities were based on the
behavior of the LS&A.faculty for three years, 1970-71 through
1972-73. The matrix is "upper triangle" (Bleau, 1981),
because all faculty either remain in the same state or move
to an upper state (Figure 2-1). Feldt's (1986) maintenance
worker example, described later in this section, provided for
senior grade workers to move back to general grade (through
demotion) at a transition rate of .05. Faculty members are
not demotable by definition of the profession and the natural
progression of faculty through states according to age

categories.

32

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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33
Johnson and.Hinman (1975) tested the following policies:
1. lowering the rate of promotion to tenure,
2. lowering the mandatory retirement age from 70 to 65,
3. restricting newly-hired faculty to tenure-track
positions only, and

4. combining the three policies above.

Additionally, the authors examined a continuation of current
policies with no changes in the overall size of the faculty
and a continuation of current policies with a 20 percent

increase and a 20 percent decrease in the size of the

faculty.

The results of the Johnson-Hinman analyses were summarized.a3
follows:
1” Given a continuation of current policies and behavior,
the LS&A faculty in 1990 would.be:
0 older, mean age 47.1 years and 46 percent over age 50
versus 43.6 years of age and 28.7 percent over age 50
in 1975;
'1 more tenured, 80.8 percent with tenure versus 77.7
percent tenured in 1975; and
'- 5 percent more expensive, with.an average salary of
$21,600 holding inflation constant versus $20,500 mean
salary in 1975.
2. The aging process is temporary, deriving from hiring

practices of the 19603. It will begin to abate in the

34

late 19803, but will be resolved only in the next

century.

13.(a) Aging is retarded only slightly by stricter
promotion rates. The chief effect of this policy is
to shift from young tenured staff to young tenure
track staff, little effect on senior, tenured
faculty.

(b) Restricting new hires to tenure track faculty has a
greater effect on reducing the average age than the
stricter promotion policy, but the study suggested
that it might result in lower quality faculty
particularly if senior faculty in key areas were to
leave.

(c) Lowering the mandatory retirement age from 70 to 65
reduces the proportion of faculty over age 50 and
the mean age, but this policy may not be well-
received by the faculty who would.desire to continue
employment past age 65.

4. A combination of all three policies would swing the
faculty distribution to the opposite extreme (i.e.,
heavily tenure track and younger), but would result in a
much lower fraction of faculty with tenure and a much
higher proportion without tenure.

5. A 20 percent reduction in the overall size of the
faculty would compound.the aging process by leading to
an average age of 49.4 in 1990 with over 54 percent of

the faculty over 50 years of age and 84.5 percent

35
tenured.

6. A 20 percent increase in the overall size of the faculty
would not dramatically affect the age distribution or
the proportion of the faculty with tenure. The average
faculty salary was slightly higher in 1990 under this
policy and the budget expenditures for a larger faculty

would have increased more than 20 percent.

Johnson and Hinman (1975) concluded that LS&A had the most
acute problem of faculty getting older and "tenuring in" at
the University. They suggested that although other policies
might exist (e.g., hiring more lectures on a short-term basis
or encouraging mobility of the senior faculty through a
revised salary policy) , such policies would likely be more
costly than the ones examined with their model. In summary,
the authors noted that they did not find "any painless

solutions to the problems at hand."

In 1979, the Dean of LS&A requested a follow-up study to the
Johnson-Hinman effort. Gross (1979) designed a study to
determine whether new policy changes under a modified model
based on more current data would be effective in reducing the
aging problem in LS&A. Based on historical data from 1969-
1978, Gross (1979) revised Johnson and Hinman's (1975) model
to more accurately reflect the movement of faculty. The
principle modifications included:

1. Gross found that 43.3 percent of newly hired tenure-

36

track faculty resigned before their seventh year and
21.6 percent were promoted before their sixth year. Only
35.1 percent followed the pattern used in the Johnson-
Hinman model where newly hired assistant professors were
assumed to spend six years in the tenure-track ranks
after which half would be promoted to tenure; of the
remainder, half would leave and half would spend a final
seventh year as assistant professor before departure.

2. The mean annual growth rate of the faculty was
determined to be -0.00892 and was substituted for the
zero growth rate, assumed in the initial study.

3. The mean ages of tenure-track faculty were found to be
significantly higher than the values assumed for the
original study. The ages of 27 through 33 years for
states 1 through 7, respectively, were substituted with
the mean ages of 30, 32, 32, 35, 34, 36, and 41 years,
respectively.

4. Historical information was also used to define new
values for the distribution of all faculty and new
hires, as well as mean salary levels and the rate of
resignation.

Four policies were evaluated by Gross, all similar to the
policies evaluated by Johnson and Hinman:

1. maintain current policy and behavior,

2. restrict new hires to tenure track positions only,

3. promote approximately 50 percent of faculty to tenure

after a strict six-year probationary period, and

3’7
4. promote approximately 25 percent of faculty to tenure
after a strict six-year probationary period, and

5. reduce faculty by 2 percent annually.

Gross assumed that none of the tenure-track faculty would
resign early under policies 3 and 4. He noted, however, that
resignation rates might rise among tenure track faculty as
opportunities for early promotion were denied. Data were not
available to substantiate this assumption and the movement of
faculty in lock-step fashion was used for policies 3 and 4 as

it had been by Johnson and Hinman for all policies.

None of the policy options investigated by Johnson and Hinman
were implemented between the release of their report in 1975
and the initial year of the Gross study, 1978. Gross found
that the 1975 study underestimated the aging and tenure
problems due to Johnson and Hinman's erroneous assumptions
concerning a stable faculty size, no early promotions, and
lower mean ages for tenure-track faculty. Yet, despite
apparently more accurate forecasts, the same general outcomes

were revealed by Gross as Johnson and Hinman.

Results from the Gross (1979) model included:
1. Regardless of the policy pursued, the proportion of the
faculty in LS&A with tenure will continue to rise, at
least until 1983. The two policies which would result in

a reduction of the tenured population beginning in 1983

38
were limiting new hires to tenure track positions and
reducing the rate of promotion to 25 percent of those up
for tenure review.

2. No policy was projected to mitigate the aging problem
with mean age shown to rise under all policies until
1993.

3. No policy was found to alter the combined cost of
faculty salaries through 1988. Restricting new hires to
tenure-track positions was projected to result in the
greatest reduction, saving approximately 2.4 percent of
the projected cost of combined salaries under a continu-

ation of the 1978 policies.

Gross concurred with Johnson and Hinman that the prospects
for mitigating LS&A's aging problem or the tenuring-in
problem were not "immediately promising.” The policies
reviewed under his model appeared to be "mildly effective
remedies to a deeply entrenched condition." Additionally, he
noted that the possible side effects of the policies were
uncertain. In fact, policies which would restrict the growth
of the tenured population or limit the rise of faculty age
could in effect greatly reduce the flexibility to make

individual appointment and tenure decisions.

Bleau's (1981) Academic Flow Model - another Markov-chain
model - was developed to project future faculty levels under

policies that grant less tenure, vary the distribution of

39
newly appointed faculty by contract type, and vary the length
of probationary periods. Sensitivity analysis found the
model to be statistically acceptable for projecting future
faculty levels of even relatively small size (72 faculty

members) .

Bleau (1981) attempted to validate the model by comparing the
actual number of faculty with the projected number after one
year. Based on chi-square goodness-of-fit tests at the .05
significance level, no statistically significant differences
were found in any of the comparisons between projected and
actual distributions by state levels, contract classifica-
tions, rank, and age if tenured. As the only validation
effort reported for faculty planning models in the literature
to date, the short time frame must be considered a severe
limitation to drawing conclusions about the internal validity

of such planning models.

The University of Southern California (USC) (Patton, 1979;
Bottomley, et al., 1980) used a computer-based simulation
model (optimization) to compare current and proposed policies
for faculties up to 250. Retirement policies, differing
lengths of probationary service, affirmative action
practices, and promotion policies with respect to rank,
salary, tenure or tenure-track status, and annual resignation
rates were studied. This model used data on 250 individual

faculty as opposed to the Markov-chain models which use age

40
distributions aggregated by state. Projections were in the
form of averages at the end of a ten-year period“ The actual
age distribution or composition of the faculty was not
provided nor could faculty flows be traced on a yearly basis

(Bleau, 1982).

The USC model was used to analyze the impact of changes in
the mandatory retirement age under policies of low and high
turnover rates and retrenchment. ”Results indicated that the
impact of changes in retirement age will vary considerably
depending upon.the initial faculty age and rank distributions
and, to a lesser extent, upon the policy assumptions made"

(Bottomley, et al., 1980).

USC has not used its faculty planning model since 1980 due to
the decentralized nature of the institution and the
assumption that most unit-level administrators can estimate
which faculty members are going to leave without using a
model (personal communication, Veronica Tincher, USC
Associate Director of Budget and.Planning, Jan. 26, 1990).
Lack of systematic information on the factors which influence
faculty retention and.attrition (Weiler, 1985) and the dete-
riorating condition of the professoriate relative to other
occupations outside academe (Bowen and Schuster, 1985) would

suggest that this sense of security may be tenuous at best.

Vaupel (1981) used mathematical equations to analyze three

37

41
ways to reduce the tenure ratio, including: increasing the
attrition of ”less-worthy" tenured faculty, lengtheningrthe
average time to tenure, and.making tenure harder to get by
reducing the proportion of junior faculty who are granted
tenure after the usual five to six year trial period. The
last option is believed to be the least desirable because
even a modest reduction in the tenure ratio from 80 percent
to 67 percent would require a reduction in the percentage of
new faculty who can be expected to be granted tenure from 50
percent to 25 percent. Lengthening the time to tenure would
be preferable since a ten-year trial would have the same
effect and would only require recruiting half as many new

junior faculty each year.

Doubling the attrition rate by holding salaries down,
providing early retirement incentives, and making promotion
from.associate to full professor more selective would.have
the same effect. According to Vaupel (1981), an increase in
the attrition rate might be the only way to reduce the tenure
ratio significantly in a period of five years or less. This
model, described by the author as "simple" is also inherently
inflexible and limited in that it fails to incorporate any
personnel policy variables and is based solely'on historical

tenure ratios and tenure and.attrition rates.

Nevison (1980) described a computer simulation model for

assessing the effects of different retirement and tenure

42
policies at Colgate University' and compared computer
simulation with Markov chain models to estimate faculty flow.
He suggested.that computer simulation models permit more
details to be included than Markov chain models. Computer
simulation models are based on the characteristics of
individual faculty and look at the changes that faculty might
undergo with certain probabilities. They are more practical
for smaller data sets due to the size and computation time.
Several independent runs of the simulation must be averaged
to get reasonable forecasts and to examine which parameters

are most critical to the results.

Markov chain models are more practical for large universities
since they assume that the proportion of faculty that move
from one classification to another is the same each year,
based on institutional policy and individual behavior.
Results of Nevison's model showed that a change in the
mandatory retirement age to 70 will have negligible effects
on tenure ratio. However, raising the tenure ratio guideline
from 55 percent to 65 percent would increase the proportion
of candidates receiving tenure from about .40 to .56 while
increasing salary costs by only 3 percent over the next 20
years at Colgate. This would provide a greater degree of

flexibility in the tenure process.

One of the few published.works on faculty planning models

43
since Bleau (1982) was Feldt's (1986) review of the general
nature of Markov models and their use in analyzing the impli-
cations of different faculty planning strategies. Even in
the mid-19803, this author based the need for faculty
planning models on the assumption that the university
workforce would have to be reduced in the future due to a
smaller pool of students, cutbacks in government support, and

rising institutional cost.

Feldt (1986) provided two policy analyses - a model of an
across-the board hiring freeze and projections of the impact
of retirement incentives, reduced promotion opportunities,
and a limited number of hires per year. Differences in the
output of the models were examined and discussed.
Additionally, the author investigated hypothetical expendi-
tures for salaries and fringe benefits for each policy and

average cost per employee.

~~~

Nevison (1981) and Bleau (1981, 1982) have found the Markov-
chain model to be the most versatile faculty planning model
since it can forecast annual faculty distributions and can be
used as a planning tool by manipulating policy variables.
According to Mortimer et al. (1985) , the majority of institu-
tions that have used faculty modeling extensively have used
Markov models. Mortimer et al. (1985) suggested that most

users of faculty models are satisfied with the models,

44
although this premise has not been systematically tested.
The authors noted that decision makers should validate their
model by checking its predictions against actual trends.
However, the review of the above articles revealed only one
published account of an attempt to validate a faculty
planning model. A summary matrix of the ten faculty planning

models described above is provided in Table 2-1.

Markov models

Markov processes are named for Andrei Andreevich Markov, the
Russian mathematician who established the framework for
modern probability theory through his work with the law of
large numbers, the central limit theorem, and stochastic
processes (Feldt, 1986; Olinick, 1978, p. 304-306). In 1907,
Markov proposed the Markov-chain model to describe, mathemat-
ically, the physical phenomenon known as Brownian motion
(Bleau, 1982) . Kolmogorov, Feller, Doeblin and other mathe-
maticians expanded the theory during the mid 19003 and Kemeny
and Snell (1960) applied the theory to the social sciences. A
review of the basic Markov chain model as provided by Forbes
(1971) and Bartholomew and Forbes (1979) is incorporated into
a more specific review of Markov models applied to faculty
planning as described by Hopkins and Massy (1981) , Mortimer

et al. (1985), and Feldt (1986) .

Markov models have been used in the social sciences to

examine the evolution of systems and determine the future

45

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47
state of systems with greater certainty. .As described in the
first section of the literature review; a Markov process
model is comprised of a matrix of a set of transition proba-
bilities” By applying the transition.probabi1ities to the
number of subjects (e.g., faculty) in each state, the members
of'a population move through a series of categories or states
from one time period to the next. Transition probabilities
are often derived from.historical data to show what would
happen if the same behavior were to continue in the future.
The utility of the model increases, however, when hypothet-
ical probabilities are introduced.to evaluate the impact of
proposed or anticipated changes in policies or subject

behavior over time (Bartholomew and.Porbes, 1979).

The modeling process with.Markov chains can best be
understood.through an example such as one modified after
Feldt (1986) and extended to include some of the mathematical
properties of the approach“ .According to Shannon (1975), the
first step in any modeling endeavor is to formulate the
problem, In the literature on faculty planning models and
Markov processes this step is not provided a good deal of
attention (most authors leap>directly into model formulation
and.data preparation). The formulation of the problem
continues throughout the study and provides a platform from
which to understand and articulate a set of germane
objectives and goals and.to define the system to be studied

(Shannon, 1975).

48

In the modified example by Feldt (1986) the problem under
consideration is that the total number of workers on the
maintenance staff at an institution is too large. The goal
is to reduce the size of the work force by at least half to
meet anticipated budget cutbacks at the institution. The
environment includes the size of the maintenance work force
but does not include the effect of the reduction on other
system components such as cleanliness of facilities, worker
satisfaction or the capacity to attract quality workers in

the future.

With a general idea of the goal of the study and the
boundaries of the system, a logical flow diagram or static
model is constructed to model the real system (Figure 2).
This diagram illustrates the universe of possibilities for
the system's state. A.maintenance worker may be in one of
three grades - entry, general, or senior - or will no longer
be employed by the institution. To keep the example simple,
Feldt (1986) assumes that maintenance workers do not move to

jobs performing other functions at the institutions.

I Promotion l Promotion ‘

New .

Hires—‘0' Entry I 9' General Ic I Senior J
l l Demotion 1 l ,

Leave Leave Leave

 

 

 

 

 

 

Fig. 2-2. Career ladder flow chart, after Feldt (1986).

49

A Markov model, like most models, needs historical data to

operate (Mortimer et al., 1985). In this example, historical

data would be collected on the number of maintenance workers

who fall into each state and.the historical probabilities of

moving from one state to another. Such probabilities are at

the heart of Markov chains. ‘Most manpower flow models use

stationary transition probabilities (Feldt, 1986) and must

adhere to the following assumptions and limitations:

1.

States are mutually exclusive and exhaustive. IEach
member of a given system must fit into only one category
(state) at a time, and, taken together, the categories
must account for all subjects (Forbes, 1971, Feldt,
1986).

The transition probabilities are stationary and constant
and each state is homogeneous and independent with
respect to transition probabilities. Thus, each member
of a state has the same probability of making a
particular transition (Forbes, 1971, Feldt, 1986).

The probability of being in any state at any one time
depends solely on the state of the system in the prior
period (Forbes, 1971, Feldt, 1986).

The system is open so that flows to and from the outside
world are permitted (Forbes, 1971).

Increasing the number of states permits a:more finely
detailed analysis. .However, each state must contain
enough subjects to ensure a large enough sample size to

meet assumption 2 above (Mortimer et al., 1985).

50
If the Markov assumptions hold, it is easy to obtain point
estimates of the transition probabilities from historical
data by the method of maximum likelihood (Bartholomew and
Forbes, 1979) . At least two years of complete stock and flow
data are required, although five or more years of data are
recommended (Spinney and McLaughlin, 1979) . Under the
assumptions above, the estimated transition probabilities are

calculated by (Bartholomew and Forbes, 1979) :

(1) P11 = znij(T) /zn_i(T) (ij = 112! o ..,k)
where the summation is taken over the periods for which data

are available under the following notations (Forbes, 1971) :

T calendar time, T = 0,1,2 e.g., T = 1979, 1980,
etc.;
k the number of states within the system, i =

1, 2, . . . , k;

ni(T) the number in state 1' at time T;

nij(T) the number of members of state i at time (T) who
are in state j at time T + 1;

pij(T) the probability that a member of state 1' makes a
transition to class j in the time interval (T,

T+1) .

Thus, with nij(T) as the observed number in 1' at T who are in
j at T + 1 and ni(T) as the stock at the beginning of this
interval, the estimate of pij can be determined for each

state. The recruitment probabilities (those who enter the

51
system) and the wastage probabilities (those who leave the
system) are estimated in an identical manner by using the
appropriate flow in the numerator (Barthelomew and Forbes,

1979) .

When the transition probabilities are placed in an array, the
transition matrix, P, for the basic markov chain model

appears as follows:

P11 P12 ' ° ' P11: ”1
P21 P22 ° ° ° P21: "2
pkl sz ° ° - Pk): wk

where again, pij is the probability that an individual in
state i at the start of the time interval is in grade j at
the end; while "1 is the probability that a member of state 1'
at the start has left by the end of the interval. Feldt
(1986) provided the following probabilities for the example

on maintenance workers:

 

 

 

To: Entry General Senior Le ave
From:
Entry grade .20 .40 .00 .40
General grade .00 .70 .05 .25
Senior grade .00 .05 .85 .10

Leave .00 .00 .00 1.00

 

52
Under this array, 20 percent of the employees in the entry
grade positions are expected to be in the entry grade a year
later; Forty percent of the entry grade employees are
expected to be promoted to general grade. None of the entry
grade employees will go to the senior grade in one year. And
40 percent of the entry grade employees will leave the
institution. The four probabilities (.2, .4, 0, .4) sum to
1.00 indicating that all possible movements for the entry

grade employees have been accounted for (Feldt, 1986).

Given that the entry year was occupied by 60 entry employees,
100 general grade employees and 40 senior grade employees and
assuming that the future flOW'Of employees among categories
will remain steady, the model can be run by integer
mathematics (Levin and.Hilpatrick, 1978). Assuming an across
the board.hiring freeze, the annual work force distributions

are obtained:

 

 

 

Base year Year 1 Year 2 Year 3 Year 4
Entry grade 60 12 2 0 0
Genera1.grade 100 96 74 55 40
Senior’grade 40 39 38 36 34
Total 200 147 114 91 74

 

Several trends are observed in this example. The number of
entry level employees quickly reduces to zero due to the

policy of'a hiring freeze and.the assumptions of static

53
promotion rates and terminations. The number of senior grade
employees is not reduced greatly due to the low attrition
rate and high opportunities for promotion of general grade
employees. Certainly the goal of reducing the number of
employees would be achieved under this policy scenario. In
fact after only two years, the number of employees would be
cut by half. Further questions might be raised in regards to
the distribution of workers among the grades. "One of the
most important advantages of a decision support model may be
the ability it provides decision makers to cycle back and ask
more clearly focused questions, ultimately resulting in more

useful analyses" (Feldt, 1986) .

This simple example provided an opportunity to explain the
logic of the Markov modeling approach and some of the basic

mathematics which serves as its foundation.

Approaches to model evaluation

Shannon (1975, p. 29) defined validation as the "process of
bringing to an acceptable level the user's confidence that
any inference about a system derived from the simulation is
correct." The importance of model validation is due to what
Shannon suggested is the ease with which most models can be
used and the willingness of casual observers to take the
results of models as truth. Consequences of accepting
erroneous results can be avoided by stating assumptions

clearly and explicitly and through careful model evaluation.

54
The problem of validating a model is no different than
validating any hypothesis or theory. Validation is one of
the most crucial aspects of any simulation study and needs to
show that the model's output does bear some meaningful rela-
tionship to what can be expected in the real world (Shannon,
1975, p. 211) . The concept of validation is not an either-or

notion but one of degree.

To ensure the validity of Markov models, Bartholomew and
Forbes (1979, p. 107) suggested three courses of action:
1. Compare the predictions of the model with actual
outcomes (usually on historical data) .
2. Carry out statistical tests of the assumptions.
3. Design the model, especially with regard to the choice
of categories, to make the assumptions as nearly correct

as possible .

Mortimer et al. (1985, p. 68) and Forbes (1971, p. 108-109)
suggested that decision makers should validate a faculty flow
model by checking its predictions against actual future
trends. As reported in an earlier section of this chapter,
Bleau (1981) validated her Academic Flow Model by comparing
model projections with the actual faculty levels using the
chi-square goodness-of-fitness test. Forbes (1971, p. 99)

also suggested the chi-square goodness-of-fitness test.

55
The chi-square statistic (Shannon, 1975, p. 76) is calculated
by:
(2) x2(i) = thNl-(T) - n,(T))2/n,<r)1,
where N1.(T) = the observed number in class 1' at
time T;

ni(T) = the projected number in class i at

If x2 = 0, then the observed and projected frequencies agree
exactly, whereas if x2 > 0, they do not. The larger the value
of x2, the greater is the discrepancy between the observed and
the expected. Shannon (1975, p. 76) identified several char-
acteristics of the chi-square goodness-of-fit test,

including:

1. Actual counts or frequencies must be used, not relative
frequencies or percentages.

2. The projected frequencies for each class must be greater
than or equal to 5. Adjacent classes can be grouped
together if there are fewer than five frequencies in any
class to get at least 5 frequencies or else the Fisher's
exact test should be used.

3. The degrees of freedom is one less than the number of
classes v = j - 1, where v = degrees of freedom, j =

number of classes .

The chi-square goodness-of-fit test is reviewed in more

detail in Chapter 3.

56
W. The two principal
assumptions of Markov chain models are that the transition
probabilities are the same for all individuals within a class
and the transition probabilities do not depend on time.
Assumptions that individuals behave independently and that
transition probabilities are functions of the current state
only are more difficult to test and less likely to be as
serious in their effects as the first two assumptions

(Bartholomew and Forbes, 1979, p. 107) .

The assumption of homogeneous classes requires that each
member of a class has the same probability of making any
transition. If a class is non-homogeneous, the probability
of a particular transition will vary from person to person
within a class. Therefore, the flow associated with this
transition will not be a Binomial variable, as assumed in the
Markov model, but will have the Binomial distribution of
Poisson (Forbes, 1971, p. 100) and the variances will be
overestimated. The comparison is made between different
categories at the same time, grade by grade. Bartholomew and
Forbes (1979, p. 107) suggested comparing different
categories by analyzing the standard errors of the flow
proportions and plotting the estimates or by using the x2
statistic for comparison of several multinomial samples.

The assumption that the transition probabilities for state 1'
remain constant over time could also be calculated by the

tests reported for the previous assumption. If the

57
transition probabilities have changed over time, then the
distributions in the columns will vary (Forbes, 1971, p.
106) . The non-homogeneity will be evidenced amongst the

columns. The statistic for testing this hypothesis is:

(3) x2 (i) = 22 111-(T) ((Pij(T)"P1-j)2) /P1j)r
~ on (T-1)(m(i)-1) degrees of freedom,
where m(i) is the number of states in j(i) and the

other notation is after Forbes (1971, p. 94).

Tests of assumptions are helpful but may not matter very much
if "the eventual effects on the predicted stocks are
negligible. It is this philosophy which underlies the wide
spread use of Markov models in many fields of application
where the assumptions, strictly (italics added) interpreted,

are certainly false" (Bartholomew and Forbes, 1979, p. 107) .

Winn. It is
most desirable to set up a model in a way that the
assumptions are more nearly satisfied. For example, if
different transition probabilities are found for different
groups in a system, then it would clearly be better to model
each group separately (Bartholomew and Forbes, 1979, p. 108) .
Any attribute which is expected to influence the transition
rates should be separated from the other. Yet, there is a

price for disaggregations. As Forbes (1979, p.100) noted,

58
the greater the number of classes, the smaller the number of

people in each class and hence the poorer the estimates.

Validation is based on statistical comparison of projected
output with observed frequencies and adherence to model
assumptions through statistical tests and the objectives of
the model building exercise. Many statistical tests are
available for validating the Markov models. Yet, as posed by
Bartholomew and Forbes (1979, p. 107) , such tests are
arguably of marginal relevance. "The objects of fitting a
model to data are to provide insights into the dynamics of

the system and to make projections.”

Overview of the literature

Ten faculty flow models were reviewed and described by
purpose, modeling procedures, results, implications, and
validation techniques. Clearly, most faculty flow models
developed during the 19703 and 19803 were devised to evaluate
the impact of policies which would reduce the proportion of
faculty with tenure and lower the median age within a
university or a unit. Different models provided varying
degrees of insight into the age, tenure classification, rank,
and salary profiles over time as a function of transition

rates which characterized specified states.

Time-dependent Markov-chain models were generally reported as

the most flexible and useful models for examining faculty

59
flow under a wide array of policy alternatives (Bleau, 1982;
Mortimer et al., 1985; and Feldt, 1986) . Forbes (1971),
Bartholomew and Forbes (1979) , Won (1976) , and others have
described the mathematical properties of the Markov-chain
model. An array of coefficients in a transition matrix
symbolizes the probabilities with which faculty members will
move to different states. By varying transition probabili-
ties based on the potential or anticipated impact of possible
policy options, faculty frequency distributions can be

projected into the future under a variety of scenarios.

The usefulness of such forecasts depends largely on the
capacity of the model to produce results which are reasonable
from the viewpoint of prospective users. The degree of
comfort with a model can be improved by systematic attempts
to ensure validity. Several scholars (Bloomfield, 1977;
Bleau, 1981; and Feldt, 1986) described approaches to
sensitivity analyses, but only Bleau (1981) reported a brief
attempt to validate a faculty flow model. Bartholomew and
Forbes (1979) reviewed three approaches to manpower model
validation, including the comparison of theoretical
predictions with actual outcomes, conducting statistical
tests of the assumptions, and designing the model so that the
assumptions are not seriously violated. The chi—square
goodness-of-fit test was noted as a widely used statistical
approach to comparing frequency distributions and testing the

validity of model assumptions.

60
The nature of Markov chain models and their application to
faculty planning has been widely reviewed in the literature.
At least ten authors have conducted policy analyses with
faculty planning models, many of which were modified after

Hopkins' (1974) Stanford model.

The importance of faculty-related decisions to colleges and
universities mandates that the basis for these decisions be
well founded and that decision makers are comfortable with
the reliability of model output. This literature review has
indicated that faculty models have not been thoroughly
evaluated and that a strong need exists to validate the
previous modeling efforts. In the following chapter, the
methodology used to develop and evaluate models in this study

is described.

CHAPTERM3
METHODOLOGY

This study was designed to estimate the impact of faculty
hiring, promotion, and separation scenarios on faculty age
class structures, tenure ratios, appointment.distributions,
and salary levels at the college level and to conduct several

case study analyses at Michigan State University (MSU).

Research Design

Three areas of study were identified in Chapter 1. The
purpose of the first area was to analyze the composition of
the faculty in each of three colleges at MSU and test for
significant difference over time (1981 to 1991) in average
age, salary, racial composition, gender, tenure ratios, and
appointment levels. IDifferences between colleges were also
of interest. The second area focused on the development and
testing of Markov chain models to project the faculty
distributions in colleges with 100 to 400 faculty members.
In the third area, the potential impact of hypothetical
adjustments to hiring and separation rates on the average
age, tenure status, academic rank, and average real salary
levels by college was projected.to the years 1996 and 2001.
Three policy scenarios were investigated for each.college.

61

62
Methodology by area
W
The purpose of this portion of the study was to analyze the
differences in the composition of the faculty over a ten-year
time frame. The target population included faculty in three
colleges at Michigan State University (MSU) -- the College of
Business, the College of Engineering, and.the College of
Natural Science. The colleges were selected because of their
relatively large sizes and their representation of
disciplines projected nationally to undergo increasingly

severe faculty shortages during the 19903.

Since the three colleges in this study were not randomly
selected from the pool of colleges at MSU, findings from
statistical analyses were not extrapolated to other colleges
within the University. For example, average age of the
faculty in the College of Natural Science would only reflect
the average age within that college, not in other colleges
within MSU or other universities. Actual or theoretical
changes over time in average age or any other factor were
also only considered relevant to the college from which the

data were collected.

Data for faculty in each college were collected through the
Office of the Provost, Academic Personnel Records. The data
set included year of birth, contractual year of employment,

racial/ethnic background, gender, term year (the year that

63
the faculty member separated from the university), term code
(the reason for separation from the university), current
academic rank, original appointment status (with or without
tenure at the time of appointment), current tenure status,
year entered the tenure system, year that tenure was granted,
year of promotion to assistant professor and associate
professor, and annual salary in 1981 and 1991. Each data set
included every tenure-track and tenured faculty member in

each respective college between the years 1981 and 1991.

The sample in this study for each college was the entire
population of faculty within each college. Some faculty
remained in the college during the time period of interest,
others left the college for various reasons, and of course
others were hired. Thus, the population in 1991 would
include some members who were on the faculty in 1981, but not
all, and would include some members who were hired after
1981. As in other studies involving time series data, the
assumption of uncorrelated.or independent error terms is not
appropriate. IRather the error terms are frequently'postively
correlated.or "autocorrelatedfl over time (Neter and

Wasserman, 1974, p. 352).

Autocorrelation can increase the probability of a Type I or
Type II error in hypothesis testing. Type II errors are more
likely to occur for data sets in which observations tend to

stay in the same classes. In this study, faculty members

64
tended to remain in the same class over time. .Although some
changes in academic ranks, tenure status, and age occurred
over time, much of the change was a result of attrition.
With Type II errors, the null hypothesis is not rejected.when
it is false. Under the set of conditions most generally
found.in this study, autocorrelation would.tend to increase
the likelihood of Type II errors, i.e., not identifying
significant differences between groups when in fact the
groups were significantly different. This limitation is
common in longitudinal studies in economics and business
(Neter and.Wasserman, 1974, p. 352) and is acknowledged as a
constraint to this study, particularly in the determination
of statistically significant differences between means - a

minor comnponent of this study.

The following descriptive statistics were determined for two
variables, age and real salary, within each college for the
years 1981 and 1991: the population size, mean, range,
standard error, and.the frequency distribution“ Individual
salaries in 1981 were adjusted for inflation with the Higher
Education Price Index to 1991 with an inflation factor of
1.7985 (Research Associates of Washington, 1991). Frequency
distributions were reported for the nominal variables of
academic rank (assistant professor, associate professor, or
professor), tenure status (tenure or tenure track),
race/ethnicity (American Indian,.Asian, black, Hispanic, or

other (white)), and gender.

65
Differences between mean age in 1981 and 1991 and between
mean real salary in 1981 and 1991 were examined under the
null hypothesis:
Ho: ’11 = 112

and the alternative hypothesis

Ha: U1 3* 112

The student t-test was used to determine statistical
differences between the means. The test statistic is
determined as follows:

t = (X1 " X2)/S§1 - 8X}:

where X1 and £2 are the sample means for population 1 (year

1991) and population 2 (year 1981), respectively, and

3531 - 3,2; =\/((3§12/n1) + (Eff/nan)

 

The level of significance, a, was set at 0.05. The smaller
a, the less will be the chance of a Type I error (mistakenly
rejecting a ”true” Ho), but the greater the chance of a Type
II error (rejecting a "false" Ho, indicating the power of the
statistical test). An a-level of 0.05 is most commonly
selected (Glass and Hopkins, 1984, p. 205) due to the balance
it gives in preventing extreme Type I and Type II errors.

For each sample size the appropriate statistic and rejection
region were then selected" Data were collected and the

statistic calculated.

66
Differences between the means for the nominal variables of
race/ethnicity, tenure status, and academic rank as
proportions of total faculty in 1981 and 1991, were tested
for significance under the null hypothesis:
Ho: 1: = K.
and the alternative hypothesis:

This hypothesis states that a proportion of the population,
1:, possessing a particular characteristic, e.g., proportion
Asian, prOportion black, proportion tenured, proportion at
the rank of professor, etc., was greater than a value K that
lies between 0 and 1. For this study, p, an estimate of 11:,
was that proportion of faculty possessing a given
characteristic in 1991 and K was the proportion of faculty

possessing the same characteristic in 1981.

Ho was tested by means of the chi-square goodness-of-fit
test, where
x2 =- 2 [(pj - Inf/1:1],

where pj = the observed proportions in a category,

1‘ .

J the expected proportions in a category.

The chi-square statistic represents the extent to which the
observed proportions differ from the expected proportions.
In this study, the level of significance, (1, was set at 0.05.

The decision criterion is that when a resulting chi-square

67
value, exceeds the critical chi-square value, then the
probability that the proportions are equal (with a = 0.05) is
less than 5 in 100 and the null hypothesis is untenable

(Glass and Hopkins, 1984) .

Results of the descriptive analyses were presented in tabular

and graphical formats in Chapter 4.

W.

This section was designed to investigate the development of a
faculty planning model after the work of Hopkins and Massy
(1981) , Bartholemew and Forbes (1979) , Grinold and Marshall
(1977), Bleau (1981), Forbes (1971), and Won (1976). Markov
chains with stationary transition probabilities were used to
develop the flow model. Under this approach, the number of
individuals in a cohort occupying a state at time t + 1
depends on the number of individuals in the various states at
time t and on the number of new entrants to the system. The
principles behind the Markov chain model and its application
to faculty flow models were reviewed extensively in the
previous chapter. As noted previously, however, the major
component of Markov model are transition probabilities which
Hopkins and Massy (1981) referred to as transition fractions

and defined in their model of faculty flow as:

pij = the fraction of faculty who move from state i to state

3‘ in a single time period

68
where pfi = the fraction who stay in the same state and

1 - Zpij = the fraction who leave the system.

Hopkins and Massy (1981) reviewed the development of
two-state and fifteen-state models, noting the advantages of
the larger model allowing ”differential rates of promotion
and attrition to be taken properly into account." Below are
the fifteen states in the model originally developed by

Hopkins (1 974) .

State Description State Description
1 Tenure track-first year 8 Tenure-age 30 to 34
2 Tenure track-second year 9 Tenure-age 35 to 39
3 Tenure track-third year 10 Tenure-age 40 to 44
4 Tenure track-fourth year 11 Tenure-age 45 to 49
5 Tenure track-fifth year 12 Tenure-age 50 to 54
6 Tenure track-sixth year 13 Tenure-age 55 to 59
7 Tenure track-seventh year 14 Tenure-age 60 to 64

15 Retirement

The Hopkins and Massy model assumes that an institution
adheres strictly to a seven-year ”up-or-out" policy for
tenure track faculty. An assistant professor at Michigan
State University, for example, is appointed for a four-year
probationary period which may be extended by three years.

Thus, the seven-year "up-or-out" policy is in effect at MSU.

The 15 states used by Hopkins and Massy may not necessarily
be the most appropriate for the current study. For example,
the authors assumed that retirement would occur at or before

age 65. Since the time of Hopkins and Massy's work,

69
legislation has abolished mandatory retirement in Michigan
and in other states across the U.S. Therefore, another state
may be required for the study at MSU. Additionally, some of
the tenure-track states might not have many members, since
most tenure-track faculty members at MSU appear to be

promoted to tenure by at least year four or five.

The matrix selected for the MSU study was based on the
purposes of the study and the relations unveiled under the
analyses in Area 1. The model was designed after Hopkins and
Massy (1981) and Bleau (1981) and provided projections of
tenure, academic rank and corresponding appointment rates

over time, by age. The states are reported below.

State Damnation

1 Tenure track-Assistant Professor-Age 26-35
2 Tenure track-Assistant Professor-Age 36-45
3 Tenure track-Assistant Professor-Age 46-55
4 Tenure-Associate Professor-Age 26-35
5 Tenure-Professor-Age 26-35
6 Tenure-Associate Professor-Age 36-45
7 Tenure-Professor-Age 36-45
8 Tenure-Associate Professor-Age 46-55
9 Tenure-Professor-Age 46-55

10 Tenure-Associate Professor-Age 56-65

11 Tenure-Professor-Age56-65

12 Tenure-Associate Professor-Age 66-75
13 Tenure-Professor-Age66-75

14 Resignation

15 Termination

16 Death

17 Retirement

Hopkins and Massy (1981) and Bleau (1981) separated tenure
track states by step with one step equal to one year as a
tenure-track faculty member. This was not deemed useful for

the MSU model because of the small number of faculty that

70
would occupy tenure track positions in the fifth through
sixth years and a higher level of interest in age of tenure
track faculty as a component of the tenure track states as
opposed to transition between tenure track states. Although,
the Bleau model included an assistant professor state for
each tenure level, the number of assistant professors with
tenure at MSU was negligible and therefore not included as

separate states in the MSU model.

The general law of motion for the Markov model was defined by

Hopkins and Massy as:

ll
..1
‘
N
‘
O
O
‘
H
.5
0

Again, pij is the probability of an individual currently in
state 1 moving to j in the next time period and fj is the
number of faculty entering state j from outside the college.
In the MSU study, p3'8 would be the probability of a faculty
member in state 3 (46-55 year old tenure track-assistant
professor) being granted tenure and thereby moving to state 8
(tenure-associate professor-age 46-55) . By definition, the

2P1j= 1, 1'. = 1, 2, ..., 17.

Bleau (1981) constructed a transition matrix for the campuses
of The Pennsylvania State University by averaging pij per
state over four consecutive years. The MSU study averaged
transition probabilities over ten years, resulting in a 13 x

17 transition matrix, M. Bleau (1981) deleted the exit

71
columns, (columns 14-17 in the MSU study), since the path
which faculty take after entering one of the exit states was
not of interest. However, the MSU study included the exit
components by assigning 0.00 probabilities to transition
fractions in states p1” to pnj , for all j = 1, 2, ..., 13
and 1.00 probabilities to transition fractions in states pbfi
to pry , for all j = 14, 15, 16, 17. The resulting

transition matrix was shown in Chapter 4.

AQ(t) was a 17-component row vector, where each component was
the faculty level by state at the start of year t. The level
for states 14-17 was valued at 0 since the number of faculty
in an exit state at each time t was 0. The 17-component row
vector, fj(t + 1), denoted the number of new appointments made
to each respective component in year t + 1, where states
14-17 were also valued at 0 since new hires were not made

directly to exit states.

Like the Hopkins and Massy and Bleau studies, the MSU
transition fractions were obtained from actual movements of
each faculty member who served.in each of the selected
colleges. A standardized array table was set up to track
each faculty member as he or she moved within a college. The
matrix multiplication and addition functions in Microsoft's
software spreadsheet package, Excel 3.0, were used to
calculate various alternative hiring and separation scenarios

described below under Area 3. The 17 x 17 matrix, M, was

72
multiplied by the 17 x 1 row vector for Ni(t) which resulted
in a 17 x 1 row vector. The number of faculty per state at
time t + 1 was determined by adding the number of new hires

per state, fj(t + 1) .

Exeseteianiactnalmmit

A rudimentary analysis of the difference between actual and
projected number of faculty by state was conducted after the
approach used by Bleau (1981) as originally investigated by
Forbes (1971) . She validated the accuracy of the Penn State
model by comparing projected faculty levels after one year
with the actual faculty levels using chi-square goodness of
fit tests. For the MSU model, the actual number of faculty
per state in 1981 were projected to 1991 under the 10-year

transition matrix.

Two goodness-of-fit tests can be used to test the degree of
agreement between the distribution of a set of empirical data
and.some specified theoretical distribution (Shannon, 1975,
p. 76, Glass and Hopkins, 1984, p. 285). Shannon (1975, p.
79) recommended.the chi-square test over the Kolmogorov-
Smirnov test for samples greater than 100. In this study,
each sample was over 100 and.the chi-square test appeared to
be appropriate» The chi-square goodness-of-fit test was
described in Chapter 2. It requires an absolute minimum of
five frequencies per interval, Lumping adjacent classes

together is acceptable in order to use the chi-square test,

73

although some power is lost.

The chi-square statistic (Shannon, 1975, p. 76; Glass and
Hopkins, 1984, p. 283)) is typically denoted as:

x2 = 2 [(12, - f,)2/r,1.

where f

O the observed frequencies in a category,

f

the expected frequencies in a category.

Recall from formula (2) in Chapter 2 that the notations used
in previous discussions of Markov models can be used in
formula (4), such that:

12 = 2 [(Niu') — ni(T))2/ni(T)].

where AQ(T) = the observed number in class i at
time T;
ni(T) = the projected number in class i at

time T.

.Alternativelyy Glass and.Hopkins (1984, p. 283) determined.x2
through the direct use of proportions, where the difference
between the observed proportion, P1! and the expected
proportirun n1, for each of the i categories is squared and
divided by the expected proportion for that category. The

sum of these quotients for all 1 categories multiplied.by the

total number of subjects, n, is x2.

12 = n - E [(p,(T) - u,<r))2/n,('r)1

74
The number of degrees of freedom, v, is 1 less than the
number of categories (r) and years (c), where v = r - c - 1.
The risk of a Type-I error, i.e., the risk of incorrectly
concluding that the null hypothesis is false when it is

actually true is set at an appropriate level, a.

If x2 = 0, then the observed and projected frequencies agree
exactly, whereas if x2 > 0, they do not. The larger the value
of x2, the greater is the discrepancy between the observed and
the expected frequency distributions. Results of the three
chi-square tests -- one for each college -- are presented in

the next chapter .

Techniques were described by Forbes (1971) to explore the
validation principles for the full range of underlying
assumptions of Markov chain models. For each college in the
MSU study, unless the 1991 projected and actual distributions
differed significantly according to the chi-square tests, it
was assumed that the major assumptions of Markov chain models
-- homogeneous classes, independent transition probabilities,
and consistency of transition probabilities over time -- were

not seriously violated.

These assumptions appeared to be satisfied in the MSU study.
For example, for a class to be homogeneous, each member must
have the same probability of making any particular

transition. Over the given time frame for which the

75
transition probabilities were derived (i.e. 10 years), a
faculty member within a state would not have a greater or
lesser chance of moving from one state to another under
current MSU Academic Personnel Policies regarding

discrimination or favoritism.

The assumption of independent flows also would not be
violated since the appointment, retirement or other exit
states are not dependent on the availability of positions on
other states. Lastly, it would not be likely that transition
probabilities varied significantly over time unless there
were specific and major policy changes which would influence
rates of hiring, promotion or retirement. Again, these
assumptions were further investigated where the 1991

projected and actual distributions differed significantly.

scenarios
The 17-state Markov model developed under Area 2 was run with
the actual 1991 faculty distributions to illustrate the
potential of the model for planning and policy analyses. The
following runs were made for each college with output
produced for the years 1996 and 2001:
1. Continue historic promotion patterns, distribution and
rate of new hires, and separation rates. This model
run would assume no major policy changes. Scenario 1

is intended to provide baseline data from which to

76
compare the results from computer runs made under the
conditions established for Scenario 2 and Scenario 3.
Continue historic promotion patterns and separation
rates but no new hires between 1992 and 1996. As
discussed in Chapter 1, budgetary shortfalls facing
universities like MSU may make it increasingly
difficult to fund new positions and/or to replace
current vacancies. Many campuses have enacted hiring
freezes in certain academic units as part of
reallocation strategies. Scenario 2 is intended to
provide insights about the impact of a policy to not
hire any new faculty over a five-year period.
Continue historic promotion patterns and distribution
rate of new hires but lower retirement rates by 10
percent for states 10 and 11 (56 to 65 year-old and 66
year-old tenured faculty) and states 12 and 13 (66
year-old and over tenured faculty) during each year of
the model run. As mentioned in Chapter 1, between 5
and 20 percent fewer faculty members retire if they
have an option to continue employment without the
constraints of mandatory retirement legislation. This
model run investigates the scenario that fewer faculty
in the 56-65 year old age and 66 and over classes will
be retiring in part as a result of laws which recently
abolished mandatory retirement based on age. Scenario
3 is intended to provide insights about the impact of

a decline in previous years' average retirement rates.

77
Output from the model runs included the following data for
each year, 1996 and 2001:
- the number of faculty per state for each of the 13
states,
N1“: + 5) and Ni(t + 10), i = 1, 2, ..., 13,
- total number of faculty,
guy“ + 5) andilNfit + 10), i = 1, 2, ..., 13,
- average overall age,

13 13
Elwin: + 5) (agei(t + 5))]/§,1Ni(t + 5), i = 1, 2, ...,

i

13,

13 13

Elwin: + 10) (age1-(t + 10))]/1§,1N1-(t + 10), 1' = 1, 2,
..., 13,

where agei(i.e., the average age of a state) was the
average actual ages of faculty in state i in 1981 and
1991 rounded to the nearest integer,

- total real salary, as determined by the average salary
per faculty per state in 1991 and projected to 1996
and 2001 at an annual rate determined for each state
by the rate of change in adjusted salaries per state
between 1981 and 1991. The 1981 salary was adjusted
to 1991 levels with the Higher Education Price Index
for faculty salaries at a rate of 1.7985 (Halstead,
1991). The salaries per state were then summed over
all states to get the total salaries adjusted to 1991
levels, for the year 1996:

real.salary(t + 5) ==§i[((salaryi(t)/(real salaryi

13
(t - 10))/2) 0 salaryi(t) -1§[Ni(t + 5)]],

78
i = 1, 2, ..., 13, where
13 13

salaryi (t) = 1§[salaryi(t) ] /1§1[Ni (t) 1

real salarY1(t -10) ==1.7985 - salaryi(t - 10), and

salary1(t - 10) = §1[salaryi(t - 10)]/1::[Nflt - 10)]
and for the year 2001:

real salary(t + 10)==:§[(salary1(t)/real salary

(t - 10)) - (salary1-(t) 0 11;:[N1-(t + 5)]],

i = 1, 2, ..., 13, where

13 13

salaryi(t) =1§i[salaryi(t)]/1=21[Ni(t)]

real salaryi(t‘-10) ==1.7985 - salaryi(t - 10), and

salaryi(t - 10) =:§,31[salaryi(t - 10)]/:1[Ni(t - 10)]
average real salary per faculty member projected to
the years 1996 and 2001 is simply the total salary
divided by the projected number of faculty members in
each college for the given years of 1996:

average real salary1(t + 5) = real salary(t + 5)/

13

2Hhfi(t + 5)]:
b4

and the year 2001:

average real salaryfit + 10) real salary(t + 10) /

Elwin + 10)],
total nominal salary, as determined by the average
salary per faculty per state in 1991 and projected to
1996 and 2001 at an annual rate determined for each
state by the rate of change in actual salaries per
state between 1981 and 1991. The 1981 salary was not
adjusted to 1991 levels with the Higher Education

Price Index for faculty salaries. The nominal

79

salaries per state were then summed over all states to
get the total salaries inflated at the rate observed
from 1981 through 1991. This rate duplicates the
inflation rate of the 19803 and might be perceived as
a prediction of inflation in the 19903. It is
intended, however, to provide an example of the
potential budgetary consequences of inflation. It is
not based on econometric assumtions, but merely
replicates the overall inflationary rate between 1981
and 1991. The calculations to estimate the projected
total salary budget in 1996 were:

nominal salary(t + 5) =§1[((salaryi(t)/(salaryi

(t - 10))/2) - salary1-(t) . 2[Ni(t + 5)]],

i = 1, 2, ..., 13, where

13 13

salary1-(t) = §1[3311?rY1(t)1/1§1[N1(t) ] agd

salary1-(t - 10) =1§1[salaryi(t - 10)]/1§[Ni(t - 10)],
and for the year 2001:

nominal salary(t + 10) = E,” (salary1-(t) /salary

(t - 10)) - (salaryi(t) - :[Ni(t + 5)]],

i = 1, 2, ..., 13, where

13 13
salaryi(t) =g1[salaryi(t)]/;[Ni(t)] and
13

1
13
salaryi(t - 10) =1§1[salaryi(t - 10)]/12:1[N1-(t - 10)]
average nominal salary per faculty member projected to
the years 1996 and 2001 is simply the total nominal
salary divided by the projected number of faculty

members in each college for the given years of 1996:

80
average nominal salary(t + 5) = nominal salary(t +
SHEINl-(t + 5)]:
and the year 2001:
average nominal salary(t + 10) = nominal salary(t +
10)/:i[Ni(t + 10)],
number and proportion tenured as determined by the
number of faculty in tenure track states 1-3 and
tenured states 4-13 as a proportion of the total
number of faculty in the year 1996,
number of tenure-track faculty“: + 5) = 12:;1[N1(t +
5){§{,N1(t + 5)] i = 1, 2, ..., 13, 13
number of tenured faculty(t + 5) = 1§1[N1(t + 5) /
Elm“ + 5)] 1' = 1, 2, ..., 13,
and the year 2001:
number of tenure-track faculty(t + 10) = 1,‘;’3,1[N1-(t +
muggy.“ + 10)] 1' = 1, 2, 13,
number of tenured faculty“: + 10) = J[12;[N1-(t + 10)/
Earl-(t + 10)] 1 = 1, 2, ..., 13,
proportion in academic ranks as determined by the
number of assistant professors (states 1-3) , associate
professors (states 4, 6, 8, 10, 12), and professors
(states 5, 7, 9, 11, 13) as a proportion of the total
number of faculty in all states, 1-13 in the year
1996,
number of assistant professors": + 5) = il[Ni(t +

13
SHANl-(t + 5)] 1' = 1, 2, 13,

81

12
number of associate professors (t + 5)=4§,1[(N,12(

5)/ ;N1(t + 5)] 1= 1, 2, ..., 13,

13
number of professors“: + 5) 5 1,2391% (t + 5)/ 211V (t +

5)] i = 1, 2, ..., 13,
and the year 2001:
3
number of assistant professors“: + 10) = 12:1[N1-(t +

13
10)/EN,(t + 10)] 1' = 1, 2, 13,

H

2
number of associate professors (t + 10) =64: gig)? {2(t +

13 ,
10)/ §Ni(t + 10)] 1' = 1, 2, ..., 13,
number of professors“: + 10)1=-S-'-_"2[Nfi(t + 10)/ EN;- (t

+ 10)] 1= 1, 2, ..., 13,

Lastly, model outputs for the runs under Scenario 1 through
the year 2001 were compared to determine if faculty distribu-
tions were significantly different between Colleges. The
chi-square goodness-of-fit test was used to compare states as

described in the preceding parts of this chapter.

Faculty distributions by state in each College were then
projected to the year 2001 with transition matrices developed
for the other two Colleges. Differences were tested for
significance with the chi-square goodness-of-fit test to
determine if a model from one college could be used to

project faculty distributions from another college.

82

Overview of the methodology

This study was divided into the following three areas:

1. Area 1 provided some descriptive statistics about the

composition of the faculty in three colleges in 1981
and 1991. The student t-test was used to test for
significant differences in average age and adjusted
salary and the chi-square goodness-of-fit test was
used to test for significant differences in proportion
tenured, proportion in different academic ranks, and
proportion by gender and race by college between the
years 1981 and 1991.

Models to project the future age, rank, tenure, and
salary of faculty members in three colleges were
developed, incorporating many of the elements used by
previous modelers (Hopkins, 1974; Bleau, 1981 and
others) . A preliminary model with 17 states was
evaluated by comparing projected faculty distributions
with actual distributions in each of three colleges
with the chi-square goodness-of-fit test. Further
modifications and evaluations were conducted as
necessary.

In Area 3, three model runs were completed per college
to assess the potential impact of different policy
scenarios. The differences in faculty distributions
by age, salary, academic rank, and tenure were tested
for significance within each college and between the

three colleges under one scenario. The transition

83
matrix for each college was used to project future faculty
distributions in other colleges and differences were tested

for significance.

Results of the analyses for each of the three areas are

presented in the following chapter.

CHAPTER4

RESULTS

Research was conducted to analyze differences in faculty
composition in three colleges at a large public university
between 1981 and 1991 and to project future faculty
composition under three hypothetical scenarios. The

following results were determined from this study.

“J... The purpose of this area was to analyze changes in
faculty composition between the years 1981 and 1991 in each
of three colleges at a large public university. Data on each
full-time faculty were collected and analyzed as described in
the methodology chapter. Differences in faculty composition
between 1981 and 1991 are described below separately for each
college and for each of the following variables: age, salary
(adjusted for inflation), rank (assistant professor,
associate professor, or professor), tenure status (tenured or

tenure track) , racial/ethnic background, and gender.

College of Business

Age. The 111 full-time faculty in the College of Business in
1981 had an average age of 42.85 years (:1: 1.069 years),
ranging from 27 years to 67 years. In 1991 a total of 132

84

85
full-time faculty members had an average age of 44.95 years
(i 0.792 years) within a range of 27 to 69 years of age. The
average ages of faculty in the College of Business between
the years 1981 and 1991 were not significantly different (p =
0.0545) based on the criteria of the one-tail, unpaired

t-test as described in the Methodology Chapter.

Whereas 36 (32 percent) of the faculty were between the ages
of 26 and 35 in 1981, 22 (17 percent) were in this age class
in 1991. Additionally, the number of faculty in the 36 to 45
and 46 to 55 year old age classes increased.between 1981 and
1991 from 34 to 53 (31 to 40 percent) and from 22 to 37 (20

to 28 percent), respectively (Fig. 4-1).

 

60

 

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>. so I 1991
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In
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1 1
o

 

 

 

 

 

 

~26 to 35 36 to 45 46 to 55 56 to 65 66 and over
Age Class

Fig. 4-1. Age class distribution of all faculty in the
College of Business, 1981 and 1991.

86
Salary, .As noted in Chapter 3, salary comparisons were made
between the average nominal salaries of all College of
Business faculty in 1991 and the average real salaries of all
College of Business faculty in 1981. The 1981 salaries were
adjusted for inflation with.the Higher Education Price Index
as provided by Research Associates of Washington (1991). The
average real salary of the 111 faculty members in 1981 was
$63,720 (1 $1,619), within a range of $32,774 to $111,343.
The average salary of the 132 faculty members in 1991 was
$65,910 (i $1,631), within a range of $35,000 to $119,500.
Although the average real salaries increased between 1981 and
1991 for all faculty members in the College, the difference
between the averages was not significant (p = .1728). The
greatest change was in the $60,000 to $70,000 salary range,
with an increase from 12 (11 percent) faculty in 1981 to 23

(17 percent) faculty in 1991 (Fig 4-2).

The real salaries of the 61 faculty members who were employed
in the College in both 1981 and 1991 were found to differ
significantly (p = .0001) in a paired t-test. The average
real salary of the 61 faculty in 1981 was $64,913 (i$2,311),
while the salaries of the same group of faculty in 1991 was
$71,675 (i$2,546). This indicates that increases in the
salaries of faculty who sustained employment with the College
of Business between 1981 and 1991, including merit increases,
exceeded inflation by about 10 percent over the ten-year

period or about one percent per year.

87
40!

 

E] 1981
I 1991

U
0|

35-

 

30-

25-

    
 

H
W
H
‘0

    

20-

 
 

15-I

Number of Faculty
H
w

    

H
H

10-

   
  
  

   

01

5

._ 2

20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100- 110- 120-
110 120 130

 
  

"

  

1
an

1

.\\\\\\\\\\\\\\\\\\\\\\\\\V:

s\\\\\\\\\\\\\‘

N»

  
 

§§§.a

 

         

Salary Range ($0003)
Fig. 4-2. Salary class distribution of all faculty in the

College of Business, 1981 and 1991 (salaries in
1981 adjusted.for inflation).

Bank. The rank distribution of faculty was found to differ
significantly between 1981 and 1991 (p = .0059). Whereas the
number of'professors and assistant professors did.not differ
substantially between the years 1981 and 1991, the number of
associate professors increased from.18 (16 percent of the
1981 total) to 45 (34 percent of the 1991 total). Rank and

tenure distributions are presented.in Table 4-1.

Tenure, .Although the percent of faculty with tenure
increased from 70.3 percent in 1981 to 80.3 percent in 1991,
this difference in the proportions was not statistically

significant at the a = .05 level (p = .0692).

88

 

Table 4-1. Observed frequencies of faculty in the College of
Business by academic rank and tenure status, 1981 and 1991.

 

 

 

 

Year

Academic

Rank 1981 1991
Assistant

Professor 33 (30%) 28 (21%)
Associate

Professor 18 (16%) 45 (34%)
Professor 60 (54%) 59 (45%)
Total 111 (100%) 132 (100%)

 

 

 

 

Year
Tenure
Status 1981 1991
Tenure
Track 33 (30%) 26 (20%)
Tenured 78 (70%) 106 (80%)
Total 111 (100%) 132 (100%)

 

RaeialLEthniefireim. Three of the five racial/ethnic
categories were represented in the College of Business in
1981 and 1991. Hispanic and American Indian faculty were not
represented in either of these years. In 1981, 95.5 percent
of the faculty were white. This proportion decreased to just

over 90.1 percent in 1991. The biggest increase in a racial/

89

 

Table 4-2. Observed frequencies of faculty in the College of
Business by racial/ethnic group and.gender, 1981 and 1991.

 

 

 

 

 

 

 

Year
Racial/Ethnic
Group 1981 1991
Asian 3 (3%) 10 (8%)
Black 2 (2%) 3 (2%)
White 106 (95%) 119 (90%)
Total 111 (100%) 132 (100%)
_

Year
Gender 1981 1991
Female 13 (12%) 19 (14%)
Male 98 (88%) 113 (86%)
Total 111 (100%) 132 (100%)

 

ethnic category was Asian which increased from about 3
percent to about 8 percent. The proportion of black faculty
remained at approximately'Z percent in 1981 and 1991 (Table
4-2). To meet the minimum cell requirement of five for the
chi-square goodness-of-fit test, the number of Asian and
black faculty members were combined and the proportion of
faculty by racial/ethnic group (white and black/Asian) was

found not significantly different (p = .1131).

90
Gender, The percent of female faculty increased from 11.7
percent in 1981 to 14.4 percent in 1991. The difference in
proportion of the male and female faculty in the College of
Business was not significantly different between 1981 and
1991 (p = .5379).

College of Engineering

Age. The average age of the 86 full-time faculty members in
the College of Engineering in 1981 was 45.01 years (i 1.005
years) within a range of 29 years and 67 years. In 1991, the
average age was 45.67 years (i .887). The average age of the
faculty in 1981 was not significantly different from the

average age of the faculty in 1991 (p = .3129).

While the average age of the faculty was not significantly
different between the two years of interest, the proportion
of the faculty in different age classes changed
substantially. The 26 to 35 year old age class showed the
greatest frequency and proportional increase, followed by
slightly less increases in the 46 to 55 and the 56 to 65 year
old age classes (Fig 4—3). The number of faculty in the 36
to 45 year old age class remained at 35 members in 1981 and

1991.

Salary, The average real salary of the 86 faculty members in
the College of Engineering in 1981 was $63,596 (1 $1,869).

The average nominal salary of the College's 126 faculty

 

 

 

 

Number of Faculty

 

26 to 35 36 to 45 46 to 55 56 to 65 66 and over

Age Class

Fig. 4-3. Age class distribution of all faculty in the
College of Engineering, 1981 and 1991.

members in 1991 was $64,569 (i $1,782). The difference in
the two average salaries was not significant (p =.3571). The
proportion of faculty members with salaries between $40,000
and $70,000 was quite consistent between the two years -- 73

percent in 1981 and 71 percent in 1991 (Fig 4-4).

The pairwise comparison of faculty salaries between the 61
members who were in the College in 1981 and 1991 indicated
that the salaries had increased significantly (p = .0001).
The mean real salary was $62,526 (1 $1,865) in 1981 while the
mean nominal salary was $71,287 (i $2,597) in 1991, a
difference of $8,761 or an increase of just over 14 percent

above inflation for the ten year period.

92

40—

 

1981

I 1991

35‘

 

304
25..
20-

15‘

Number of Faculty

10-

   

5‘ . 3 2
l A 7

20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100- 110- 120-

110 120 130

    
   

1
no:

 

 

 

 

Salary Range ($0003)

Fig. 4-4. Salary class distribution of all faculty in the
College of Engineering, 1981 and 1991 (salaries in
1981 adjusted for inflation) .

Bank. The proportion of faculty in the College of
Engineering by rank did not differ significantly between 1981
and 1991. While the proportion of faculty in the rank of
professor declined from 55 percent to 45 percent, the
proportion of faculty in the ranks of associate professor and
assistant professor increased from 28 percent to 34 percent
and from 17 percent to 21 percent, respectively. The
frequency distributions for rank and tenure in the College

are shown in Table 4-3.

93

Tenure, The proportion of the faculty in the College of

Engineering with tenure fell from 82.6 percent in 1981 to

79.4 percent in 1991.

Conversely, the proportion of faculty

in a tenure track increased from 17.4 percent to 20.6

percent. The difference in proportion tenured was not

statistically significant (p = .5633) .

 

Table 4-3. Observed faculty frequencies in the College of
Engineering by rank and.tenure status, 1981 and 1991.

 

 

 

 

 

 

 

Year
Academic
Rank 1981 1991
Assistant
Professor 15 (17%) 26 (21%)
Associate
Professor 24 (28%) 43 (34%)
Professor 47 (55%) 57 (45%)
Total 86 (100%) 126 (100%)
w
Year
Tenure
Status 1981 1991
Tenure
Track 15 (17%) 26 (21%)
Tenured 71 (83%) 100 (79%)
Total 86 (100%) 126 (100%)

 

94
W. Four of the five racial ethnic groups
were represented on the College of Engineering faculty in
1981, including approximately'82 percent white, 15 percent
.Asian, 1 percent black, and 1 percent Hispanic. ‘By 1991, the
proportion of white faculty had.decreased to just over 80
percent while the proportion of Asian and.Hispanic faculty
had increased to approximately 18 percent and 2 percent,
respectively, No black faculty were on the faculty in the

College of Engineering in 1991.

In order to meet the chi-square test requirement of at least
five elements per cell, the number of Asian, black, and
Hispanic faculty were combined into one category. The
proportion of faculty in the two groups (white and the sum
total of Asian, black, and.Hispanic faculty) was not
significantly different between 1981 and 1991 (p = .6611).
The frequency distributions by racial/ethnic group and.gender

are presented in Table 4-4.

Gender, The College of Engineering had no female faculty
members in 1981. Thus a statistical test to compare the
change in proportion of faculty by gender was not possible.
In 1991 the number of female faculty in the College had
increased to a total of five, approximately 4 percent of the

126 total full-time faculty.

95
College of Natural Science
Age. Unlike the College of Business or the College of
Engineering, the average age of the faculty in the College of
Natural Science was significantly greater in 1991 than in
1981 (p = .0006). The average age of the 334 faculty members

in 1981 was 46.87 years (i 0.512 years), while the average

 

Table 4-4. Observed faculty frequencies in the College of
Engineering by racial/ethnic group and gender, 1981 and 1991.

 

 

 

 

Year

Racial/Ethnic

Group 1981 1991
Asian 13 (15%) 23 (18%)
Black 1 (1%) 0 (0%)
Hispanic 1 (1%) 2 (2%)
White 71 (83%) 101 (80%)
Total 86 (100%) 126 (100%)

 

 

 

Year
Gender 1981 1991
Female 0 (0%) 5 (4%)
Male 86 (100%) '121 (96%)

 

Total 86 (100%) 126 (100%)

 

96
age of the 342 faculty members in 1991 was 49.383 years (i

0.518), a difference of approximately 2.5 years.

The histogram in Fig 4-5 shows that the highest proportion of
faculty members shifted from the 36 to 45 year old age class
in 1981 to the 46 to 55 year old age class in 1991. The 36
to 45 year old age class decreased from 128 (38 percent) of
the faculty in 1981 to 92 (27 percent) in 1991. Conversely,
the 46 to 55 and the 56 to 65 year old age classes increased
from 99 (30 percent) and 63 (19 percent) in 1981, respective-
ly, to 120 (35 percent) and.89 (26 percent), respectively, in
1991. In 1981 just over 50 percent of the faculty in the
College of Natural Science were 46 years old and above. By

1991, over 64 percent of the faculty were age 46 and above.

 

 

140
E] 1981
120

120
>1
:1 100
:I
3
m 80
'H
o 1
g 60
z 40

20

0

 

 

 

26 to 35 36 to 45 46 to 55 56 to 65 66 and over
Age Class

Fig. 4-5. Age class distribution.of all faculty in the
College of Natural Science, 1981 and 1991.

97
Salary. Another difference between this college and the
other two colleges in the study was that the average real
salary for the 334 faculty members in 1981 was significantly
higher than the average nominal salary for the 342 faculty
members in 1991 (p = .049). The average salary in 1981,
adjusted for inflation, was $61,664 (i $907) and the average
salary in 1991 was $59,483 (i $953), a difference of $2,181.
The major difference between the two points in time was that
while the highest proportion of faculty in 1981 earned
between $50,000 and $60,000 in 1981, the highest proportion

in 1991 earned between $40,000 and $50,000 in 1991 (Fig 4-6).

110—

 

Z 1981

87 || 1991

100-

     

 

 

 

   

Number of Faculty

   

 

20-30 30-40 40-50 50-60 60-70 70-80 80-9090-100 100- 110- 120- 130- 140-
110 120 130 140 150
Salary Range ($0003)

Fig. 4-6. Salary class distribution of all faculty in the
College of Natural Science, 1981 and 1991 (salaries
in 1981 adjusted for inflation).

98
Although, average faculty salaries in the College of Natural
Science fell behind inflation by about 3.54 percent over the
ten year period, average salaries of those individuals who
remained in the College from 1981 through 1991 increased
significantly (p = .0001). This indicates that the average
salaries of new faculty members hired.during the ten year
period were not as high as those faculty members who
separated from the College during the ten year period. In
the paired comparison, faculty who remained.over the ten year
period.had average salaries of $59,865 (1 $1,033) in 1981 and
$63,440 (i $1,151) in 1991. The average increase of $3,575
per faculty member represents a 5.97 percent increase above

the rate of inflation over the ten year period.

Bank, The proportion of faculty by rank in the College of
Natural Scienceidid.not differ significantly between 1981 and
1991 (p = .1469). The proportion of faculty at the rank of
professor stayed about the same, while the proportion at the
rank of associate professor decreased from 22.5 percent in
1981 to 17.8 percent in 1991 and the proportion at the rank
of assistant professor increased from 9.0 percent in 1981 to

12.6 percent in 1991 (Table 4-5).

Iennre, The proportion of faculty in the College of Natural
Science with tenure decreased from 91.3 percent in 1981 to
86.0 percent in 1991. Conversely, the proportion of

tenure-track faculty increased from 8.7 percent to 14.0

99

percent over the ten year time frame. The difference in the

proportions was significant at the a.= 0.05 level (p =

.0285).

 

Table 4-5. Observed faculty frequencies in the College of
Natural Science by rank and tenure status, 1981 and 1991.

 

 

 

 

 

 

 

Year
Academic
Rank 1981 1991
Assistant
Professor 30 (9%) 43 (13%)
Associate
Professor 75 (22%) 61 (18%)
Professor 229 (69%) 238 (70%)
Total 334 (100%) 342 (101%)
_
Year
Tenure
Status 1981 1991
Tenure
Track 29 (9%) 48 (14%)
Tenured 305 (91%) 294 (86%)
Total 334 (100%) 342 (100%)

 

100
RaeialLEthniefirdnn. While the proportion of white and Asian
faculty remained virtually the same between 1981 and 1991,
the proportion of black faculty members increased from 1
percent in 1981 to 2 percent in 1991, the proportion of
Hispanic faculty members decreased from 0.6 percent to 0.3
percent, and the proportion of American Indian faculty
members increased from 0 percent to 0.3 percent (Table 4-6).
In order to meet the minimum requirement of five elements per
cell for the chi-square goodness-of-fit test, the number of
faculty in the black, Hispanic and American Indian groups
were combined. The proportion of faculty in the white,
Asian, and combined black, Hispanic and American Indian
groups was not significantly different between 1981 and 1991
(p = .5843).

Gender, The number of female faculty members increased from
23 in 1981 to 40 in 1991, while the number of male faculty
members decreased from 311 to 302. As a proportion, females
and.males comprised 6.9 percent and 93.1 percent,
respectively, of the faculty in 1981, and 11.7 percent and
88.3 percent, respectively, of the faculty in 1991. The
difference between the proportion of male and female faculty
members in the College of Natural Science was found to differ

significantly (p = .0315) between 1981 and 1991 (Table 4-6).

101

 

Table 4-6. Observed faculty frequencies in the College of
Natural Science by racial/ethnic group and gender, 1981 and
1991.

 

 

 

 

Year

Racial/Ethnic

Group 1981 1991
American Indian 0 (0%) 1 (0%)
Asian 27 (8%) 27 (8%)
Black 3 (1%) 7 (2%)
Hispanic 2 (1%) 1 (0%)
White 302 (90%) 306 (89%)
Total 334 (100%) 342 (100%)

 

 

 

 

Year
Gender 1981 1991
Female 23 (7%) 40 (12%)
Male 311 (93%) 302 (88%)
Total 334 (100%) 342 (100%)

 

m The purpose of Area 2 was to develop a model for
each college that would reliably project faculty
distributions by state over time. Each.model was tested.by
projecting the number of faculty per state from the initial
year used to develop the model to 1991. The projected.va1ues

were then compared with the observed values.

102
.As reported in Chapter 3, a 17-state format was selected that
would allow for the projection of the distribution of faculty
by state into the future and.the subsequent determination of
the age, rank, tenure status, and salary levels of the

faculty. The states are reported below.

Statenessrintien

1 Tenure track-Assistant Professor-Age 26-35
2 Tenure track-Assistant Professor-Age 36-45
3 Tenure track-Assistant Professor-Age 46-55
4 Tenure-A330ciate Professor-Age 26-35
5 Tenure-Professor-Age26-35
6 Tenure-Associate Professor-Age 36-45
7 Tenure-Professor-Age36-45
8 Tenure-Associate Professor-Age 46-55
9 Tenure-Professor-Age46-55
10 Tenure-Associate Professor-Age 56-65
11 Tenure-Professor-Age56-65
12 Tenure-Associate Professor-Age 66-75
13 Tenure-Professor-Age66-75
14 Resignation
15 Termination
16 Death
17 Retirement

The number of faculty per state was determined for each
college in each year between 1981 and 1991. The number of
faculty remaining in a given state in a given year and the
number that moved to another state in a given year were
determined. The proportion of faculty which remained in
given state and moved from that state to another state were
determined resulting in ten matrices with annual transition
probabilities. The transition probabilities were averaged
over the ten years to give a transition matrix for testing.
This procedure was repeated for each college resulting in

three sets of transition matrices.

103
College of Business. The transition matrix developed with
transition probabilities for the College of Business over the
ten-year time period did not provide an acceptable level of
performance. .Although the 1981 faculty levels per state
projected to 1991 with.the model were not significantly
different from the actual 1991 levels (x2== 9.954; p =
0.1912), the level of confidence was not particularly strong.
The model overestimated the number of faculty that would
occupy states 1, 2, and.7 in 1991 and.underestimated.the

number of faculty that would occupy states 6 and 8.

After review of the faculty distributions by state during the
19803, it was noted.that the transition and.biring rates in
the early part of the time frame were substantially different
from rates between 1988 and 1991. For example, the number of
faculty in state I declined from a level of about 32 faculty
members in 1982 through 1987 to 18 in 1988. Many of these
faculty moved to state 4 or state 6 in a one year time
period. The number of faculty in state 2 increased from 4 in
1981 to 15 in 1988. Such a dramatic change in transition
rates was not captured in the ten-year average and the high
number of hires to state 1 (about 8 per year between 1982 to

1987) declined dramatically over the 1988 to 1991 time frame.

Although the ten-year model appeared.to be moving the number
of faculty per state closer to the actual number observed in

1991, the model did not appear to have adjusted quickly

104
enough, a result of the effects of averaging over a single
time period with.a major change in transition rates and

hiring rates between 1987 and 1988.

Transition probabilities had been determined with transition
rates averaged over as few as two and four years by other
modelers (Hopkins, 1974; and Bleau,1981, respectively). For
the current study, transition rates over three years, 1988 to
1991, were averaged to develop a transition matrix for the
College of Business (Fig. 4-7). Average number of hires per

state per year are also included in the figure.

To enhance the model, rates for several of the states for the
College of Business were modified from their original values.
For example, between 1988 and 1990, no faculty members in the
College occupied states 5 or 12, although the possibility
existed for these states to be occupied, In actuality, state
5 became occupied in 1991. To move faculty members through
these states, the average rates for state 5 over the ten year
period, 1981 to 1991, were used, while rates similar to
transition rates in state 13 were used for state 12, since
they both included.tenured faculty members in the same age
bracket, 66 years and above. Transition rates for states 8
and 10 averaged 1.0 for the three year time frame meaning
that faculty members in these states would.never move to
another state. This of course was unrealistic but had

resulted from the few number of faculty occupying these

105

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106
states and.by chance that they did not move from these states
over the period for which.the rates were averaged. Rates for
state 8 were determined from the rates averaged over the ten
year time frame. Rates for state 10 which remained at 1.0
even when averaged.over the ten year time frame were modified
to reflect rates in state 11, occupied.by tenured faculty in
the same age bracket. These modifications appeared.realistic
under the circumstances and.given that these states were for
the most part occupied.by a small number of faculty members
in this college. Table 4-7 below'provides the number of
faculty projected.by the model from 1988 to 1991 and the

observed number per state in 1991.

 

Table 4-7. Projected and observed number of
faculty per state in the College of Business, 1991.

 

 

State Projected 1991 Observed 1991
1 14 15
2 8 8
3 4 3
4 7 6
5 0 1
6 30 29
7 17 16
8 8 10
9 26 25

10 2 2
11 15 16
12 0 0
13 1 1

 

Total 132 132

 

107
To conduct the chi-square goodness-of-fit tests, several
states were combined.to meet the requirement of five values
per cell. For the data in this college, state 3 was combined
with state 2, state 5 was combined with state 7, states 12
and 10 were combined with state 8, and state 13 was combined
with state 11. The chi-square goodness-of-fitness test
indicated that the null hypothesis could.not be rejected at
the a = 0.05 level (x2 = 0.832; v = 7.- p = 0.9971) and the

model was used.to project faculty distributions under Area 3.

College of Engineering. The College of Engineering
transition matrix developed by averaging the transition
probabilities for each year over the 1981 to 1991 time frame
is presented in Fig. 4-8. The only modification to this
matrix was to state 12. As with the College of Business
matrix, no faculty members occupied state 12 during the given
time frame. To ensure that faculty moved through this state
in the event that they were hired or moved to the state from
another state, the average transition rates for state 13 were
used for state 12. The number of faculty per state projected
by year from 1981 to 1991 resulted in the values in Table

4-8, page 105.

Several states were combined in order to meet the minimum
cell requirements of the chi-square goodness-of-fit tests.
State 3 was combined.with state 2. States 10 and 12 were

combined.with state 8. State 13 was combined with state 11.

108

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109

 

Table 4-8. Projected and observed number of faculty
per state in the College of Engineering, 1991.

 

 

 

State Projected 1991 Observed 1991
1 21 20
2 8 5
3 1 2
4 7 8
5 0 0
6 18 21
7 12 9
8 11 10
9 24 27
10 2 3
ll 21 19
12 0 0
13 2 2
Total 127 126

 

Results of the chi-square goodness-of-fit test revealed that
the null hypothesis could not be rejected at the a = 0.05
level (x2 = 2.577; v = 8; p = 0.9581) and the model was used

for projecting faculty distributions under Area 3.

College of Natural Science. A transition matrix was
developed for the College of Natural Science by averaging
transition probabilities per state per year from 1981 to 1991
(Fig. 4-9) . As with the College of Business and the College
of Engineering matrices, transition rates for state 12 were
modified by using rates found in state 13. Average

transition probabilities for state 12 over the ten year time

110

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111
frame had resulted in a 1.0 transition probability from state
12 to state 17 (retirement). Therefore, any faculty member
who entered state 12 would immediately retire. Although it
is feasible that a tenured faculty member at the associate
professor rank and over 66 years of age would be highly
likely to retire, it appears equally reasonable to assume
that some faculty would opt not to move from state 12 and the

rates were modified accordingly.

Applying the matrix to the faculty distribution per state in
1981 and moving the faculty forward.by year to 1991 resulted

in the projected distribution in Table 4-9. As shown in

 

Table 4-9. Projected.and.observed.number of
faculty per state in the College of Natural Science.

 

 

State Projected 1991 Observed 1991
1 26 23
2 21 21
3 3 4
4 10 7
5 0 1
6 31 36
7 36 35
8 10 8
9 108 107

HP
HO
.1:
U1

82 85

HH
com
o
o

11 10

 

Total 342 342

 

112
Table 4-9, the projected distribution was quite similar to
the observed distribution. After combining state 3 with
state 2, State 5 with state 7, and states 10 and 12 with
state 8 to meet the requirements of the chi-square
goodness-of-fit test, the differences between the observed
and projected values were found not significant and the null
hypothesis could not be rejected at the a = 0.05 level (x2 =
2.376; v = 8; p = 0.9673) . The model in Fig. 4-9 and the
hiring distribution in the final column were used for
projecting faculty distributions in the College of Natural

Science as described in Area 3.

m The purpose of Area 3 was to use the models
developed under Area 2 to project faculty distributions by
state to the years 1996 and 2001 under three hypothetical
scenarios. As discussed in previous chapters the scenarios
are as follows:

1. Continue historic promotion, appointment, hiring and
separation rates. Under this scenario, each model
developed under Area 2 would be run without further
modification. New faculty members would enter the system
according to the average annual hiring rates reported in
Fig. 4-7, 4-8 and 4-9.

2. Continue historic promotion and separation rates, but set
the hiring rates to 0 for all states from 1992 through
1996, then resume historic hiring rates in 1997.

3. Continue historic hiring and promotion rates, but alter the

97

113
separation rates for states 10-13 to reflect a 10 percent
reduction in retirement rates over the ten year time frame,

1991 to 2001.

The models were run for each college according to the
methodology described in Chapter 3. The resulting faculty
distributions by state are presented below for each College
under each scenario, along with average age, average and
total real and nominal salary, and rank and tenure
distributions. The resulting distributions and averages from

each scenario for each college are discussed in Chapter 5.

College of Business

The resulting faculty distributions by state from.the
modeling efforts for the College of Business are presented
for each scenario in Table 4-10. Average faculty age, total
and average salary (nominal and real), and.proportion by rank
and.tenure status as projected for the years 1996 and 2001

for the College of Business are presented in Table 4-11.

As shown in Table 4-10, the total number of faculty in the
College was projected.to decrease slightly under Scenario 1;
decrease greatly under Scenario 2 in the first five years
when hiring is eliminated, leveling off at the reduced level
through 2001; and remain at the same level under Scenario 3
when the retirement rate was lowered. The average age of

faculty in the College under each scenario was projected to

114

 

Table 4-10. Faculty distributions projected for 1996 and
2001 under three scenarios, College of Business.

 

 

 

 

 

1996 2001
Scenarios Scenarios

State 1991 1 2 3 1 2 3
1 15 12 5 12 11 9 11

2 8 5 2 5 4 3 4

3 3 3 3 3 3 2 3

4 6 5 3 5 4 3 4

5 1 0 0 0 0 0 0

6 29 27 24 27 23 19 23

7 16 12 9 12 10 8 10

8 10 15 15 15 17 16 17

9 25 29 27 29 30 27 30
10 2 4 4 5 6 6 7
11 16 16 15 18 17 16 21
12 0 0 0 0 0 0 0
13 1 1 1 1 1 1 1
Total 132 129 109 132 127 111 132

 

remain about the same over the ten-year time frame,
increasing by one to two years depending on the scenario.
When adjusted for inflation, average salary per faculty
remained about the same under each scenario, ranging from a
low of $66,711 under Scenario 1 in 2001 to a high of $67,485
under Scenario 2 in 1996. .All average salaries, adjusted for
inflation, were projected to be higher than the average
salary of $65,910 in 1991. The $8.7 million total salaries

in 1991 decreased slightly under Scenario 1 and increased

115

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116
slightly under Scenario 3. Total real salaries decreased

under Scenario 2 to $7.4 million in 1996 and 2001.

To provide some indication of the potential average and total
nominal salaries in the future, it was assumed that nominal
salaries per state would continue to increase at 1981 to 1991
rates. Under this assumption average nominal salaries in the
College of Business were projected to increase to about
$95,000 in 1996 and $125,000 in 2001, with minimal
differences between averages projected under the three
scenarios. Total nominal salaries were projected to fluctuate
more widely; For example, total salaries were projected.to
increase by $8.0 million.by 2001 under Scenario 3. Total
nominal salaries under Scenario 2 were projected to increase
by $5.2 million over the same time frame, a difference of

$2.8 million from the total projected under Scenario 3.

Under all scenarios, the percent of faculty who were
assistant professors and therefore in tenure-track positions
was projected to be lower than the percent currently found in
these positions in 1991. The most severe decrease was
observed under Scenario 2 where no new faculty were hired
between 1992 and 1996. Concurrently, the percent of faculty
with tenure and therefore at the associate professor and full
professor ranks was projected to increase to about 85 percent
under Scenarios 1 and 3 in 1996 and 86 percent under

Scenarios 1 and 3 in 2001. Under Scenario 2, the percent of

117
faculty at the tenure rank was projected to increase to
nearly 91 percent in 1996, dropping to just over 87 percent
in 2001.

College of Engineering

The resulting faculty distributions by state from the
modeling efforts for the College of Engineering are presented
for each scenario in Table 4-12. Average faculty age, total
and average salary (real and nominal), and proportion by rank

and tenure status as projected for the years 1996 and 2001

 

Table 4-12. Faculty distributions projected for 1996 and
2001 under three scenarios, College of.Engineering.

 

 

 

 

1996 2001
Scenarios Scenarios

State 1991 1 2 3 1 2 3
1 20 21 6 21 22 17 22
2 5 8 2 8 8 6 8
3 2 1 1 1 1 0 1
4 8 8 5 8 8 5 8
5 0 0 0 0 0 0 0
6 21 21 15 21 21 14 21
7 9 12 11 12 14 10 14
8 10 14 14 14 17 14 17
9 27 26 25 26 28 25 28
10 3 3 3 4 4 3 4
11 19 24 23 25 27 26 29
12 0 0 0 0 0 0 0
13 2 3 3 3 3 3 3

 

Total 126 141 108 143 153 123 155

 

118

for the College of Engineering are presented in Table 4-13.

The number of faculty members in the College of Engineering
was projected to change considerably from the initial levels
of 1991 under each scenario. For example, by the year 2001,
the number of faculty in the College was projected to
increase by 27 and 30 under Scenarios 1 and 3, respectively.
Under Scenario 2, the number of faculty members was projected
to decrease by 18 in the year 1996, but increase to 123 in

2001, 3 fewer than in the original cohort in 1991.

As shown in Table 4-13, the relative changes in the
characteristics of the College of Engineering faculty were
similar to changes which were projected.to occur in the
College of Business for each given scenario. For example,
average age was projected to increase slightly under all
scenarios, with the highest increase under Scenario 2 where

no faculty were hired for a five year period.

Average salary per faculty member adjusted for inflation was
projected to be higher under each scenario than the $64,569
average salary in 1991. The highest average salary was found
under Scenario 2 reflecting a decrease in the number of
faculty in the states with lower average salaries. Average
real salaries under Scenario 3 were slightly higher than
average real salaries under Scenario 1 reflecting a lower

retirement rate for those older faculty in the states with

119

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120
higher average salaries. Total real salaries were projected
to increase substantially under Scenarios 1 and 3, reflecting
large increases in the total number of faculty in the
College. By 1996, total real salary under Scenario 2 dropped
from the 1991 level of $8.1 million to $7.5 million but

increased to about $8.6 million in 2001.

Average nominal salary was projected.to increase to about
$93,000 per faculty member in 1996 and $123,000 per faculty
member in 2001 under Scenarios 1 and 3. The average salary
per faculty member under Scenario 2 was projected to increase
to over $98,000 in 1996 and $125,000 in 2001. Total salaries
were projected to range widely between Scenarios 1 and 3 and
Scenario 2. 'Whereas, total salaries would reach over $13
million in 1996 and about $19 million in 2001 under Scenarios
1 and 3, total salaries would increase to $10.6 million in

1996 and $15.4 million in 2001 under Scenario 2.

Under Scenarios 1 and 3, the proportion of faculty by rank
and tenure status were not projected to change substantially
over time from the 1991 proportions. Approximately 20
percent of the faculty were projected to be at the rank of
assistant professor in 1996 and 2001 under Scenarios 1 and 3.
The hypothetical hiring freeze between 1992 and 1996 resulted
in a projected decrease in the percent of faculty at the
assistant professor level to about 8 percent in 1996.

Following the lifting of the hiring freeze in 1997, the

121
percentage of faculty at the assistant professor level was
projected to increase to about 19 percent by 2001 under

Scenario.2.

College of Natural Science

The resulting faculty distributions by state from.the
modeling efforts for the College of Natural Science are
presented for each scenario in Table 4-14. .Average faculty
age, total and.average salary (real and.nominal), and

proportion by rank and tenure status as projected for the

 

Table 4-14. Faculty distributions projected for 1996 and
2001 under three scenarios, College of Natural Science.

 

 

 

 

1996 2001
Scenarios Scenarios

State 1991 1 2 3 1 2 3
1 23 26 5 26 26 22 26
2 21 22 9 22 22 16 22
3 4 4 3 4 4 3 4
4 7 9 4 9 10 7 10
5 1 O 0 0 0 0 O
6 36 32 23 32 32 20 32
7 35 33 29 33 32 23 32
8 8 10 9 10 11 8 11
9 107 100 95 100 94 85 94
10 5 4 4 4 3 3 4
11 85 88 86 91 87 84 92
12 0 O 0 0 O 0 0
13 10 12 12 13 12 12 14

 

Total 342 340 279 344 333 283 341

 

122
years 1996 and 2001 for the College of Natural Science are

presented in Table 4-15.

The total number of faculty was projected to remain about the
same under Scenario 3 and to decrease slightly under Scenario
1. States 1, 2, and 4 were projected to undergo slight
increases under Scenarios 1 and 3, with decreases projected
in the number of faculty in states 6, 7, 9, and 10. The
decreases in state 9 were projected to be especially large.
Changes to states and overall faculty size under Scenario 2
were projected.to be similar to changes found in other
colleges. Under Scenario 2, the College could expect large
decreases in the lower states and varying decreases in the

number of faculty in most higher states.

Average age of faculty members in the College of Natural
Science was projected to remain at around 49 years under
Scenarios 1 and 3 (Table 4-15, page 123). As in the other
two colleges, average age was projected to be slightly higher

under Scenario 2.

The average real salary per faculty member was projected to
decline under all scenarios except Scenario 2 where the
average salary was shown to increase slightly in 1996 but
fall below the 1991 average by the year 2001. Total salaries
adjusted for inflation were projected.to be lower than the

total salary in 1991 under all scenarios. The projected

123

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124
decrease reflected the changes in faculty salaries between
1981 and 1991 at rates below the historical rate of inflation
for many of the transitional states. Therefore, althouqh
faculty members' salaries increased over time, this increase
for some faculty in the College of Natural Science had not
been as fast as the rate of inflation and was projected to

continue as such in this model.

Average nominal salary was projected to increase to about
$80,000 by 1996 under Scenarios 1 and 3 and to about $83,000
under Scenario 2. By 2001, average faculty salaries in the
College of Natural Science were projected to increase to just
over $100,000. Nominal salary totaled for all faculty
members in the College was projected to reach about $27
million under Scenarios 1 and 3 by 1996 and $33.7 million and
$34.5 million, respectively, by 2001. Due to the hiring
freeze and subsequent reduction in the size of the faculty
cohort under Scenario 2, the total nominal salary was
projected to increase to only $23.2 million in 1996 and $28.9

million in 2001 under this scenario.

The proportion of faculty members by rank was not projected
to undergo substantial changes under Scenarios 1 and 3.
Results from the models under these scenarios indicated that
the percent of faculty at the assistant professor level would
increase to about 15 percent in 1996 and continue at that

rate through 2001. The percent of faculty at the associate

125
professor and professor levels were projected to decrease
slightly under Scenarios 1 and.3. Similar relations were
revealed for tenure rank, where the percent of faculty with
tenure decreased to about 85 percent under Scenarios 1 and 3

in both 1996 and 2001.

Under Scenario 2, nearly 80 percent of the faculty were
projected to be at the rank of professor by 1996. Only 6
percent of the faculty would be at the assistant professor
rank. Nearly 94 percent of the faculty would have tenure.
By the year 2001, both rates were shown to decrease with
about 72 percent of the faculty at the professor level and

just over 85 percent with tenure.

Stabilizing faculty size over time

Earlier in this paper it was noted that "replacement demand"
as defined by Cartter (1976) included factors related to the
net migration of faculty into and out of the faculty labor
market. Of particular interest in this regard was the number
of faculty that would be needed to replace the faculty who
were separating from a given college. In this study, the
number of new hires which would be needed to balance the
number of separators per year under Scenario 1 through the

year 2001 was determined by college and by state.

As shown in Table 4-16, approximately 5.05, 4.20, and 13.30

faculty members would need to be hired each year in the

126

 

Table 4-16. .Historical hiring rates and projected hiring
rates (number of faculty per year) to maintain a stable
faculty size under Scenario 1 between the years 1991 and
2001, by college.

 

 

 

 

College of College of College of

Business Engineering Natural Science

State Historical Adjusted Historical Adjusted Historical Adjusted
1 2.25 2.53 4.90 2.78 7.30 7.77
2 0.75 0.84 1.30 0.74 2.60 2.77
3 0.00 0.00 0.00 0.00 0.30 0.32
4 0.00 0.00 0.10 0.06 0.30 0.32
5 0.00 0.00 0.00 0.00 0.00 0.00
6 0.25 0.28 0.60 0.34 0.50 0.53
7 0.75 0.84 0.20 0.11 0.60 0.64
8 0.00 0.00 0.00 0.00 0.00 0.00
9 0.25 0.28 0.20 0.11 0.70 0.74
10 0.00 0.00 0.00 0.00 0.00 0.00
11 0.25 0.28 0.10 0.06 0.20 0.21
12 0.00 0.00 0.00 0.00 0.00 0.00
13 0.00 0.00 0.00 0.00 0.00 0.00
Total 4.50 5.05 7.40 4.20 12.50 13.30

 

College of Business, College of Engineering, and College of
Natural Science, respectively, to maintain the number of
faculty at 1991 levels through the year 2001. The proportion
of faculty hired per state during the 1991 to 2001 time
period, was set at the same proportion used to develop each
respective model from 1988-1991 for the College of Business
and 1981-1991 for the College of Engineering and the College

of Natural Science.

In comparison to the historical hiring rates, it was found

that if the total number of faculty hired into the College of

127
Engineering were reduced.by just over three faculty per year,
the faculty size would remain at around a total of 126
through 2001. On the other hand, an additional faculty
member would need to be hired every other year to maintain a
stable faculty size of 132 in the College of Business under
Scenario 1. ILikewise, an additional four faculty members
would need to be hired every five years in the College of
Natural Science as a supplement to the current hiring rates
in order to maintain a stable faculty size of 342 through the
year 2001. As in all the modeling exercises in this study,
these results are contingent upon consistent transition
probabilities in all states over time, an assumption which

shall be discussed further in the final chapter.

Comparison of model output and models

A.brief analysis was completed to compare projected faculty
distributions from.the model runs between colleges and to
test whether a model developed for one college could be used
to project reliable faculty distributions with data from

other colleges.

Several researchers have developed models designed to account
for future faculty flow for an entire institution (Hopkins,
Biedenweg, Bleau). If faculty distributions and transition
rates from state to state were significantly differently
between colleges, then.these models would not likely account

for most differences between colleges nor provide information

128
relevant to decision making processes at the college level.
To test the differences in faculty distribution between
colleges, output from the three models under each scenario
were compared with the chi-square goodness-of-fit test. For
example, the proportion of faculty in each state in 1996
under Scenario 1 was compared between the 3 colleges in this
study. It was found that the proportions in each of six
comparisons differed significantly (p = 0.0001) , with

chi-square values ranging from 49.7 to 55.1.

Secondly, faculty distributions in each college were
projected to 2001 under Scenario 1 by using transition
matrices from the other two colleges. For example, the
initial distributions and hiring rates by state from the
College of Business were run with the transition matrix
developed for the College of Engineering and then run with
the transition matrix developed for the College of Natural
Science. This approach was repeated for each College. The

resulting distributions can be found in Table 4-17.

Each distribution projected with other colleges' models was
significantly different from the distribution projected with
the College's original model. The closest fit was found when
the model for the College of Engineering was used to project
distributions in the College of Business (x2 = 19.581; v = 7;

p = 0.0065) .

129
Overview of results
Several characteristics of faculty members in 1981 were
significantly different from characteristics of faculty
members in 1991. These differences varied by college,

although average real salaries of faculty who remained in a

 

Table 4-17. Projected faculty distributions in the year 2001
under Scenario 1 using models from each college with data
from that college and the other two colleges.

 

Number of faculty per state in the Colleges of:
Business Engineering Natural Science

 

 

 

projected to 2001 with models developed for the Colleges of:

 

   

 

State B E NS E B NS NS B E

1 11 10 8 15 23 18 26 34 32

2 4 5 7 6 7 12 22 12 15

3 3 1 1 1 3 1 4 9 3

4 4 4 3 5 8 7 10 12 11

5 0 0 0 0 0 0 0 1 1

6 23 14 13 16 29 21 32 44 33

7 10 15 18 12 7 18 32 14 25

8 17 17 7 15 17 7 11 26 25

9 30 34 42 27 25 37 94 79 77

10 6 4 3 4 6 3 3 9 6

11 17 29 28 26 16 26 87 60 100

12 0 0 0 0 0 0 0 1 0

13 1 3 3 3 1 3 12 3 12
Combined

States B E NS E B NS NS B E

1 ll 10 8 15 23 18 26 34 32

2/3 7 5 8 6 10 13 26 21 17

4 4 4 3 5 8 7 10 12 11

6 23 14 13 16 29 21 32 44 33

5/7 10 16 18 12 7 19 33 15 26

8/10/12 24 21 9 19 23 10 14 35 31

9 30 34 42 27 25 37 94 79 77

11/13 18 32 31 29 16 29 99 63 112

 

Where, B - College of Business; E - College of Engineering; and NS - College of
NaturalScience.

States were combined in lower half of table to meet requirements of the chi-square
goodness-of—fittest .

 

130
college from 1981 to 1991 were found to be significantly
higher in 1991 for all three colleges. The other difference
which was statistically significant in the College of
Business included:
0 proportion of faculty by academic rank (increase in the

number of associate professors from 1981 to 1991) .

Significant differences in the College of Natural Science
between 1981 and 1991 included:

0 average faculty age (increase of 2.5 years),

0 average real salaries of all faculty (decrease),

- proportion tenured (decrease), and

- proportion of faculty by gender (increase in the

proportion of females on the faculty).

Differences in characteristics of faculty in the College of
Engineering were not statistically significant between 1981
and 1991, other than the aforementioned differences in the
average adjusted salaries of faculty who were in the college

in both 1981 and 1991.

A Markov transition matrix was developed for each college and
found to project faculty distributions over time which were
not significantly different at the a = 0.05 level from
distributions observed for each college. Comparison of the
projected outputs of the models indicated that projected

faculty distributions differed significantly between

131
colleges. .Additionally, when a model from one college was
used to project faculty distributions in another college, the
result was always significantly different from the original
projections determined with the college's original model. It
was determined that a model should only be used for the

college for which it had been originally developed.

Using each model developed for each college, the number of
faculty by state was projected.over time under three
hypothetical scenarios. The results of these projections
indicated that some important changes could be expected over
the next ten years, the level of significance of these
changes varying by college, time, and scenario. It was also
determined.that in order to:maintain a stable size faculty
through the year 2001 under the assumptions of Scenario 1,
the number of hires per year in the College of Business and
the College of Natural Science would.have to be increased
above historical rates, while the College of Engineering
could lower its hiring rates by over three faculty per year

and.conceivably maintain a stable faculty size.

The implications of these results in decision making and
policy analysis at the college and university levels are
summarized and.discussed.in<greater detail in the following

chapter.

CHAPTERS

SUM! AND DISCUSSION

Project overview

The American Council on Education recently reported that many
colleges and universities in the United States are unable to
fill full-time faculty positions in computer science,
business, mathematics and the health professions (El-Khawas,
1989) . This shortage is expected to worsen in these four
areas and to widen and include a range of academic
disciplines over the next ten years. Nearly two-thirds of
all colleges and universities are reporting that it takes
longer to find qualified persons for full-time faculty
positions and that it is more difficult to get top applicants
to accept faculty positions offered to them (El-Khawas,

1990) . This proportion has doubled in only two years.

Such shifts in the academic labor market are products of what
Cartter (1976) calls replacement demand and enrollment
demand. Replacement demand includes those factors related to
faculty retirement and the net migration into and out of
academic careers. Enrollment demand pertains to the overall
impact of college enrollments and student-faculty ratios on
the faculty labor market.

132

133
The principal objectives of this study were: (1) to review
the changes in composition of the faculty in three colleges
of a large public university during the 19803 in terms of
faculty size, age, gender, racial/ethnic background, tenure
distribution, and academic rank, (2) to develop a model that
could be used on Macintosh computers to project the number of
faculty by age class, tenure status, academic rank, and
salary level in academic units with 100 or more faculty, (3)
to conduct several case studies projecting faculty
distributions in five-year time periods under different
hiring, promotion, and separation scenarios, and (4) to
analyze the policy implications of the different case-study
scenarios on faculty size, age class distribution, and
budgets. The model would be validated by comparing observed
and theoretical distributions for faculty cohorts in the

selected academic units.

Markov chains with stationary transition probabilities were
used to develop time-dependent models for tracing faculty
flows in each college. A 17-state model, designed after
Hopkins and Massy (1981) and Bleau (1981) , provided
projections of tenure status and academic rank and

corresponding appointment rates over time, by age.

Transition probabilities were averaged over ten years,
resulting in a 13 x 17 transition matrix, M. Transition

fractions were obtained from actual movements of each faculty

134
member who served in each of the selected colleges. A
standardized array table was set up to track each faculty

member as he or she moved within a college.

Differences between actual and projected number of faculty by
state were tested for significance by comparing 1981 faculty
levels projected over 10 years with the actual faculty levels

using chi-square goodness-of-fit tests.

Three model runs were made with the actual 1991 faculty
distributions projected to the years 1996 and 2001:

1. Continue historic promotion patterns, distribution and
rate of new hires, and separation rates. This model
run would assume no major policy changes.

2. Continue historic promotion patterns and separation
rates but no new hires between 1992 and 1996.

3. Continue historic promotion patterns and distribution
rate of new hires but lower retirement rates by 10
percent for 56 to 65 year-old faculty during each year

of the model run.

Scenario 1 was selected to provide a baseline of faculty
distributions to compare output from the other two model
runs. Scenario 2 was selected due to the current fiscal
crisis in the state of Michigan and limited institutional
flexibility for future cost-saving measures other than to

continue not to fill vacant faculty positions. Evidence for

135
Scenario 3 was provided by Lozier and Dooris (1991) who found
that 20 percent of 400 surveyed faculty members would have
continued employment past age 70 if mandatory retirement had
not been in effect. An arbitrary rate of 10 percent was
selected to fit somewhere between the 5 percent who actually
deferred retirement after age 70 at institutions with no
mandatory retirement and the 20 percent who in response to a
hypothetical question Lozier and Dooris (1991) would have
deferred retirement past age 70 if mandatory retirement had

not been a factor.

This study was designed to provide insight into the potential
effects of various hiring, promotion and separation decisions
on the composition of tenure system faculty. It was not
intended to supersede current policies designed to ensure
equal opportunity for employment, promotion and advancement.
Academic personnel policies are the result of years of
academic discourse and experience and are typically adopted
by governing boards for the protection of personnel and the
institution. Models such as the one developed and used in
this paper are meant to point out the long-term importance
and potential consequences of personnel policies not to
displace them. As such, this study and its results should be
limited to studying institutional personnel systems not to

displace them .

136

Other limitations of the study included:

The generalizability of the results of this study was
limited to each academic unit included in the study
and not to other academic units within Michigan State
University or other institutions.

The three faculty cohorts included only tenure system
faculty in a large public university where the faculty
are not unionized. Part-time faculty, instructors and
lecturers, and graduate teaching assistants were not
included in the study, although they are assuming
greater roles and becoming more prevalent in some
colleges and universities.

The model is deterministic and assumes that mean
transition probabilities provide perfect information.
As averages, these values may not capture important
policy decisions in a given year and tend to mask
significant changes in a given year as a result of
averaging.

Parametric tests were used to determine the
significance of statistical differences between means
and proportions although the populations were neither
random nor independent, increasing the chance of a
Type II error and lowering the chance of rejecting a
false null hypothesis.

Standard errors about each mean transition probability
were not used to calculate confidence intervals for

the projected number of faulty per state.

137
° The model was based on the assumption that faculty
transition rates will continue to remain relatively
stable over time when in fact they may not.
- Lastly, this study examined only replacement demand
and did not examine enrollment demand. As such,
enrollment demand in this study was assumed to be

constant over the given time frame.

Sumery and discussion of results

m. Selected characteristics of the faculty in 1981 were
compared with the faculty in 1991. The most consistent
difference was that faculty members who were present in a
college in 1981 and 1991 had greater average real salaries in
1991 than in 1981. In each college, average salaries of
faculty members employed during the period of interest
exceeded inflation significantly. Unlike salaries of faculty
in the College of Business and the College of Engineering,
the average faculty salary of those individuals who remained
in the College of Natural Science increased by nearly 6
percent above inflation from 1981 to 1991, the overall
average salaries for all faculty members in the College fell

behind inflation by about 3.5 percent.

In all three colleges, average faculty age was higher in 1991
than in 1981, although the difference was significant only in
the College of Natural Science. Also, whereas the average

age of faculty in the College of Business and the College of

138
Engineering was around 45 years in 1991, the average age was

approaching 50 years in the College of Natural Science.

The age distributions of faculty in 1991 were similar to the
national distributions forwdoctoral universities which showed
little recent change in the proportion of faculty above age
65 but some major increases in the proportion of faculty
between the ages of 40 and 55 (El-Khawas, 1990, 1991). For
example, between 1981 and 1991, the percent of faculty 46
years old and above increased from 37 to 43 percent in the
College of Business, from 43 to 50 percent in the College of
Engineering, and from 51 to 64 percent in the College of
Natural Science (i.e., nearly two thirds of the faculty in

the College of Natural Science are age 46 and above).

This type of buildup of faculty members in the older age
classes across the nation led.Bowen and Schuster (1986) and
others to forecast high rates of retirement and an inadequate
supply of faculty to keep up with.high attrition rates during
the late 19903. A premise of this study was that such
national projections may not be particularly relevant to
individual campuses or academic units without looking at
other factors including historical hiring and separation

rates. These factors are discussed later in this chapter.

The proportion of faculty by academic rank changed

significantly in the College of Business with a large

139
increase in the number and proportion of faculty at the rank
of associate professor. .A similar change was noted in the
College of Engineering, although the difference between the
proportions was not statistically significant“ Rank
distribution in the College of Natural Science remained

fairly consistent over the ten-year time frame.

Whereas about 45 percent of the faculty were at the rank of
professor in the College of Business and the College of
Engineering in 1991, 70 percent were at this rank in the
College of Natural Science. The greater proportion of
professors in the College of Natural Science can likely be
attributed to the greater proportion of older faculty in the
College and.the more traditional nature of the discipline.
In this regard, the Colleges of Business and.Engineering
would be more likely to include midcareerists and more
individuals with a greater variety of professional
opportunities in today's job market. Thus, the smaller
percentage of professors in these two colleges might be due
in part to the greater likelihood of these tenured faculty
separating from academe to pursue careers with industry or
government than tenured faculty in the College of Natural

Science.

Tenure distributions were similar to the patterns of faculty
by academic rank. .Approximately 80 percent of the faculty in

the College of Business and the College of Engineering had

 

140
tenure in 1991, about 86 percent of the faculty in the
College of Natural Science had received tenure, a significant
decrease from 1981 when 91 percent of the faculty had tenure.
The difference between the proportion of the faculty tenured
in 1981 and 1991 was statistically significant in the College

of Natural Science only.

The proportion of faculty in the Colleges by racial-ethnic
group remained largely unchanged over the time period and no
differences were statistically significant. The total number
of black, Hispanic, and American Indian faculty (typically
noted as underrepresented minority groups) in all three
colleges was 9 in 1981 and 14 in 1991. The number of Asian
faculty increased from 3 to 10 in the College of Business,
from 13 to 23 in the College of Engineering, and remained at
27 in the College of Natural Science. The proportion of
white faculty was 90 percent in the College of Natural
Science and the College of Business in 1991 and 80 percent in

the College of Engineering.

In 1991, 14 (2.3 percent) of the 600 faculty in the three
colleges were black, Hispanic, or Native American. This
represents a slight increase from the 9 black, Hispanic, and
Native American faculty representing 1.7 percent of the 531
faculty members in the three colleges in 1981. Despite
special incentives from the University's central

administration for its colleges to hire more minorities,

141
particularly in the late 19803, change in minority
representation in these three colleges was small by any
standard. And although the proportion of underrepresented
minorities increased by 35 percent during the given time
frame, the resulting total of 14 black, Hispanic, and Native
American faculty out of a total of 600 faculty is far short
of meeting even the least stringent affirmative action goals.
This tends to confirm the paradigm on the stability of higher
education as described in Chapter 1. As described by Hopkins
(1974) even small changes in faculty demographics must be

preceded by major changes in hiring and retention practices.

Differences in the proportion of faculty by gender was
statistically significant for the College of Natural Science,
with the proportion of females increasing from 7 percent to
12 percent. The proportion of females in the College of
Business was 14 percent in 1991, up from 12 percent in 1981.
The percent of females on the faculty in the College of
Engineering increased from 0 percent in 1981 to 4 percent in

1991.

Similar to the racial/ethnic distributions, small changes
were observed in gender distributions over the 1981 to 1991
time frame. In regard to fulfilling affirmative action
goals, these changes were moving in the proper direction.
The percent of all faculty in the 3 colleges who were female

increased from about 7 percent in 1981 to about 11 percent in

142
1991. And although this represents a 57 percent increase in
the proportion of female faculty members in the colleges, the
11 percent of females on the faculty in proportion to the 52
percent of the general population comprised of females
indicated that female representation is still not adequate in

these colleges.

Overall, each college in 1991 was comprised of a slightly
older faculty body, most of which was comprised of white,
males who were tenured and.at the rank of associate professor
or professor. Their average salaries tended to range from
$60,000 to $65,000 depending on the college. Small shifts
were noticeable in the age class distribution between 1981
and 1991 with the largest increases in the 46 to 55 year old
age group and the 56 to 65 year old age group. More Asians
were on the faculty in 1991 than in 1981, with a smaller
increase in the total number of black, Hispanic, and.Native
American facultyu More female faculty members were in the

three colleges in 1991 than in 1981.

A:3._2., Models were constructed for each college. The model
for the College of Business used.data from an abbreviated
time frame, 1988 to 1991, due to significant changes in the
middle of the decade that could.not be accounted for with a
model built over the ten year time frame. Models for the
College of Engineering and College of Natural were developed

with data transformed into transition probabilities and

143
averaged over the 1981 to 1991 time frame. Hiring
distributions were also averaged over the respective time

periods.

Faculty distributions in each college were projected by state
from the original year of initiation to 1991. Differences
between the observed and projected distributions were not
statistically significant and the models were deemed reliable
for the purposes outlined under Area 3. It is important to
note, however, that a better test of the reliability of the
models would be to compare the distributions projected for
1996 or 2001 with the actual distributions in 1996 or 2001,
because the ”strongest verification of any model occurs when
we demonstrate that the model can successfully predict events
which have not yet transpired" (Shannon, 1975, p. 231) . Even
though the models appeared to adequately reproduce the past
faculty flows, it sill remains to be shown whether they will
faithfully predict the future. And of course such a test can
not be performed until 1996 when the actual faculty
distributions can be compared with those projected to 1996 by

each model .

MILL The projections made with each model provided some
valuable information for decision makers interested in
faculty characteristics and budgetary issues. For example,
no college was projected to undergo extreme changes in the

W of the faculty under any of the three scenarios.

144
In fact, the average age was projected to be very stable in
the Colleges of Engineering and Natural Science under
Scenarios 1 and 3, remaining at around 46 and 49 years,
respectively. The average age of the faculty in the College
of Business was projected.to increase to about 46 years in
1996 and to 47 years in 2001 under both Scenarios 1 and 3.
Under Scenario 2, which froze faculty hires for five years
and in effect reduced the number of faculty in the younger
states, average ages were only slightly higher than those
projected under Scenarios 1 and 3 reaching a maximum of 51.4
years in the College of Natural Science in 1996 before

decreasing to 50.1 years in 2001.

Although average age was not projected to increase
significantly over the next five or ten years for any of the
colleges, the number of faculty in the older age classes
continued to build. The number of faculty in the 66 year old
and above age class in each College under Scenario 1 was
projected to increase slightly by the year 2001, while the
number of faculty in the 56 to 65 year old age class was
expected to increase greatly in the College of Business (Fig.
5-1) and the College of Engineering (Fig. 5-2), but less so
in the College of Natural Science (Fig. 5-3). One could
surmise that an increasing number of faculty will be retiring
shortly after the year 2001, although projections more than

ten years into the future become increasingly tenuous.

145

College of Business
60

 

50

 

 

40

 

30

20

Number of Faculty

10

 

26 to 35 36 to 45 46 to 55 56 to 65 66 and over

Age Class

Fig. 5-1. Age class distribution of faculty in the College of
Business, 1981, 1991, and 2001 projection --
Scenario 1.

 

College of Engineering

 

 

 

 

Number of Faculty

 

 

26 to 35 36 to 45 46 to 55 56 to 65 66 and over

Age Class

Fig. 5-2. Age class distribution of faculty in the College of
Engineering, 1981, 1991, and 2001 projection --
Scenario 1.

146
College of Natural Science

 

 

 

 

Number of Faculty

 

26 to 35 36 to 45 46 to 55 56 to 65 66 and over

Age Class

Fig. 5-3. Age class distribution of faculty in the College of
Natural Science, 1981, 1991, and 2001 projection --
Scenario 1.

Average_real_salazie§ were projected to increase slightly
under all scenarios for the College of Engineering and the
College of Business and decrease slightly under all scenarios
for the College of Natural Science through the years 1996 and
2001. Differences in projected average faculty salary
between colleges reflected the actual changes in faculty
salaries between 1981 and 1991, which were greater than
inflation in the College of Engineering and the College of
Business but less than inflation in the College of Natural
Science. Care must be taken, however, not to assume that the
lower average salary in the College of Natural Science is a
result of disproportionate salary increases between the three

colleges. It has been noted that the average salary of

147
faculty members who were in the College of Natural Science in
1991 was greater than the average adjusted salary of faculty
members in 1981. The average adjusted salaries for all
faculty decreased, however, indicating that faculty who were
hired.between 1981 and 1991 had lower salaries than faculty

who separated from the College since 1982.

Iota1_real_sa1ar¥.as projected.to 1996 and 2001 was quite

variable between and within colleges and scenarios. This was
one of the more important variables in that it reflected.the
change in a major budget item and was adjusted for inflation
to 1991 to provide a baseline for comparative purposes. For
example, under Scenario 1 in the College of Business, it was
projected that total salaries would decrease slightly over

the next ten years when adjusted.to 1991 levels. However,

under Scenario 3, the total adjusted salary was projected to

increase slightly.

The decrease in total salary under Scenario 1 can be
attributed to a small decrease in the number of faculty in
the College of Business in 1996 and 2001. The decrease may
have been greater, however, if the proportion of faculty with
tenure and.at higher-paying academic ranks had not increased.
Although the total number of faculty stayed about the same
under Scenario 3 for the College of Business through the
years 1996 and 2001, the increase in the proportion of

faculty with tenure and at higher-paying academic ranks was

 

148
high enough to result in an overall increase in projected

faculty salaries .

Therefore, as expected, both the projected number of faculty
in a college and the projected rank of the faculty tended to
be very important in the projection of total real salary
under the various scenarios. The greatest increase in total
real salary was projected under Scenario 3 in the College of
Engineering due predominantly to the large projected increase
in the total number of faculty by the year 2001 and in part
to the increase in the number of faculty in higher academic
ranks. Under this scenario, the total adjusted salary in the
College of Engineering would increase by almost 31 percent or
$2.5 million by the year 2001. Under Scenario 1, however,
which continues historical transition rates, the College of
Engineering would still experience an increase in total

adjusted salary of nearly 30 percent or $2.4 million.

W and total nominal salaries in the
year 2001 were projected to be about double the 1991 averages
and totals. It must be repeated, however, that such
projections were based on inflationary rates and salary
increases identical to the rates experienced during the
19803. It would be highly improbable for the same rates to
occur over the 1992 to 2001 time frame. The projections are
intended to merely provide an example of the salary levels

and budgetary totals which would occur under each scenario if

149
inflation and salary increases were to be maintained at the
1981 to 1991 levels. For example, average nominal salaries
of $125,000 per year were projected for the College of
Business and the College of Engineering by the year 2001
under any scenario. Average nominal salary for faculty in
the College of Natural Science would just exceed $101,000 per
year by 2001. If inflation is lower than that experienced
during the 19908, then nominal salaries will lower than the
salaries projected with the model. Also, changes in salary
rates are a function of administrative policies and college
resources and will have great influence on changes in the

average salary levels in the 19903 and beyond.

IotaLnominaLsalary combined across all three colleges under

Scenario 1 was projected to reach $68.3 million by the year
2001, an increase of over $30 million or 84 percent from the
1991 total of $37, .1 million. Under the constraints of this
study (i.e., that inflation and salary increases would
continue through the years 1996 and 2001 at the 1981 to 1991
historical rates), university planners and business officers
should be aware that to sustain the three colleges in this
study at historical hiring and promotion levels, annual
average budget increases for salaries of 8.4 percent will be
necessary. On the other hand, hypothetical hiring freezes
under Scenario 2 would result in a total projected nominal
salary combined across all three colleges of $58.2 million by

the year 2001, a 57 percent increase from the 1991 total.

150
This would require about a 5.7 percent increase per year in

this budget item to satisfy the conditions under Scenario 2.

DifferenceslufluunuLscenarios. ‘Using Scenario 1 as the
baseline, the projected changes in variables related to age,
salary, rank, and tenure for Scenarios 2 and 3 followed
similar trend lines for each college. For example, if no new
faculty members were hired in any of the three colleges
between 1992 and 1996, as under Scenario 2, it was projected
that by 1996, the average age, average adjusted salary,
percent of faculty tenured, and.the percent of faculty at the
ranks of professor and associate professor would increase. As
pointed out previously, most faulty are hired into the
younger, lower rank states and reducing their number in
effect increases the relative proportion of older faculty in
higher rank.positions. Of course, the hiring freeze under
Scenario 2 also reduces the total number of faculty per
college by the year 1996, which leaves fewer faculty on the

payroll and a lower total adjusted salary.

Equally important, the distribution of faculty members in
tenure-track positions would become nearly depleted leaving
less than 10 percent of the faculty in these positions. This
might be expected to further exacerbate the buildup of
faculty in the older age classes exhibited in Figures 5-1,
5-2, and 5-3. By the year 2001, however, many of the extreme

changes in faculty distribution found under Scenario 2

151
through the year 2001 had become much less prominent and the
averages tended.to move back toward the averages under

Scenarios 1 and 3.

Scenario 3 showed slight increases over Scenario 1 in terms
of every characteristic except percent of the faculty in
tenure-track positions and at the assistant professor level.
Since Scenarit>3 merely reduced the retirement rate by 10
percent, the increase in the number of faculty in the higher
ranked positions was small and therefore had a small impact
on the general composition of the faculty and related
characteristics. One difference which had budgetary
implications was in total real salary which.was projected to
be about $2.0 million dollars greater by the year 2001 under

Scenario 3 than under Scenario 1.

Stabilizianacnlthizemuime. As discussed in Chapter

1, many researchers have forecast impending faculty shortages
by the late 19903 resulting from increases in the number of
faculty who are expected.to retire and a concurrent lack of
new faculty to replace the retirees. A major question
related to this forecast is how many faculty would.be needed

to maintain the number of faculty at a given level?

Based on historical promotion and separation rates, it was
determined that about 22 faculty would have to be hired per

year in all three colleges to maintain the future number of

152
faculty at 1991 levels (approximately 5 faculty per year in
the College of Business, 4 in the College of Engineering, and
13 in the College of Natural Science). This would require a
slight increase in the current hiring rates for the College
of Business and the College of Natural Science, but the
hiring rate in the College of Engineering could be decreased
by about three faculty members per year. Policies to increase
or decrease the total number of full-time tenure system
faculty members in a college would need to consider

adjustments from the above rates.

Precautions

It was determined that a model developed for one college was
not adequate for use in projecting faculty flow in another
college. This of course might have important implications
for models developed for use across an entire institution.
Colleges or other academic units are often quite different
from one another in terms of promotion, appointment,
separation, age, salaries and other rates and
characteristics. A model combined across units would tend to
mask these differences and fail to capture the faculty flows
unique to a given college over a given time frame. The fact
that many decisions related to personnel and personnel
compensation are made at the college level is equally
important to confine the development and.use of a faculty

flow'model.to a relatively homogeneous academic unit.

153
Output from modeling efforts is often regarded more highly
than it should be. University- and college-level
administrators sometimes have a natural temptation to take
projections from a model at face value, although it would be
unwise in this case or any other to do so. Projections of
future outcomes are based on past events -- events which are
unlikely to occur again at the same rates or in the same
manner. Yet, history is a significant and useful guide to
the future. And, as noted in the opening chapter, higher
education offers one of the more stable environments in which

to develop manpower planning models.

In light of these precautions, faculty flow models provide
valuable early warning systems to alert decision makers to
the consequences of changes to an academic unit. The
challenge to the user of the model is to develop the capacity
to visualize the future in order to identify and select
hypothetical scenarios which are indeed relevant to the
nature of the academic unit of interest. Like other models,
the model utilized in this study merely provides a tool for
optimizing an administrator's knowledge and experience in
anticipating structural and organizational changes to the

system at hand.

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