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Modelling Faculty ReplacementStrategies Using A Time‐dependentFinite Markov‐chain ProcessE. Raymond Hackett a , Alexander A. Magg a & Sarah D.Carrigan aa Auburn University , USAPublished online: 07 Jul 2006.

To cite this article: E. Raymond Hackett , Alexander A. Magg & Sarah D. Carrigan (1999)Modelling Faculty Replacement Strategies Using A Time‐dependent Finite Markov‐chainProcess, Journal of Higher Education Policy and Management, 21:1, 81-93, DOI:10.1080/1360080990210107

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Journal of Higher Education Policy and Management, Vol. 21, No. 1, 1999 81

Modelling Faculty Replacement Strategies Using ATime-dependent Finite Markov-chain Process

E. RAYMOND HACKETT, ALEXANDER A. MAGG &SARAH D. CARRIGAN, Auburn University, USA

ABSTRACT A time-dependent Markov-chain process was used to model faculty replacement strategieswithin a college at a research university. This investigation suggests that a stochastic modelling approachcan provide valuable insight when planning for personnel needs in the immediate Jive to ten year future.

Introduction

The approach of the year 2000 is providing an apt background for planning the futureof higher education. At all levels, institutions of higher education are reinventingthemselves. A changing knowledge base, new methods of delivery, new populations toserve, changing resource patterns, and a rapidly changing faculty and staff are focusinginstitutions on planning as never before. Planning for the higher education enterprise,and developing appropriate and related policies, are activities that create an institution'sfuture. Central to both planning and policy development is making decisions. Ideally, aninstitution supports decision making by providing the best possible information to reduceuncertainty before making a decision. Over the last several decades several sophisticatedanalytical strategies have been developed to support policy analysis and planning forhigher education. However, use of the most appropriate uncertainty-reducing analysis,given a particular decision, is more the exception than the rule. Institutions must becomemore intentional at adopting and applying available decision support strategies. Thispaper examines the use of one most powerful personnel forecasting techniques, atime-dependent Markov-chain model (Reid & Taylor, 1989), for college-level planningfor faculty replacement. This stochastic modelling strategy is extensively employed inmilitary and corporate labour force planning but is rarely used in higher education.In this study the technique is applied, its predictive validity assessed, and the efficacy ofusing such a technique discussed.

The widespread concern about faculty shortages has yet to be realised. However, somestudies are now indicating that a significant percentage of faculty eligible to retire aredoing so (Stein & Trachtenberg, 1993). The discussion of faculty replacement needs has

1360-080X/99/010081-13 © 1999 Association for Tertiary Education Management

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82 E. R. Hackett et al.

centred on national trends and aggregate data. Yet, the replacement of faculty occurs atthe institution, within the college and department. The need for faculty is institutionspecific, college specific, department specific and can vary widely (Elms, 1992). Monitor-ing faculty flow and predicting future faculty needs are becoming more important at thecampus and college level. Understanding the parameters of personnel continuity andthe probability for change has remained a challenge for human resource management.The degree of accuracy in personnel forecasting can have campus-wide implicationsbeyond recruitment activities. Other campus activities that can be affected by potentialchanges in academic staffing include benefits planning and policy, personnel policies andtheir effects on faculty retention rates, academic programme planning, and evenclassroom productivity measures.

Review of the Problem and Literature

Carter (1976) defined two concepts significant to faculty planning: replacement demandand enrolment demand. Replacement demand includes those factors related to netmigration into and out of academic careers. Enrolment demand concerns the impact ofcollege enrolments on faculty labour markets.

Bowen and Schuster (1985, 1986) describe several conditions that influence replace-ment demand: real and perceived decline in compensation; salary compression; shifts ininstitutional priorities and reward systems; the conditions in the labour market outsidethe university; and increasing pressure on faculty at all levels to research and publish.Elms (1992), investigating the faculty replacement demands of a research university,concluded that retirement is not an isolated variable but instead one variable related tofaculty replacement within a complex social matrix.

Enrolment demand is necessarily defined in terms of individual institutions andprogrammes. Certainly, environmental factors such as demographics impact enrolmentlevel. However, a number of other factors, some that the institution can control and somethat it cannot, also help determine enrolment trends at an institution. A brief listincludes: the strength and clarity of the institution's mission, the effectiveness of therecruitment programme; the effectiveness of the retention programme; the reputationand viability of individual academic programmes; the strength of the institution's studentlife programme and co-curricular activities; and the institution's location (Erdmann,1990; Straker, 1991; Woodard, 1995).

It would seem clear that any investigation of the personnel needs of the academicprogramme of an institution must account for institutional policies and plans. However,all policy investigations reside on some core assumptions. In the case of academicpersonnel planning, the primary assumption is that there are college-level facultydynamics that can be modelled. Such modelling should first begin with an analysis ofhistorical data to produce a model for replacement needs and then include parametersfor alternative personnel plans and policies (Reid & Taylor, 1989).

The development of faculty planning models received attention during the 1970s whensignificant shifts in enrolment patterns were evident, related to an increased studentinterest in professional curricula (Bleu, 1981). Models developed during these years totrack the flow of faculty through rank, and in and out of academe, were defined asfaculty flow models by Hopkins & Massey (1981). These models can be used as planningtools to investigate the various institutional practices that can affect the number of facultypositions to be filled. Mathematical models for forecasting personnel needs have beencentral to the field of human resource planning (McClean, 1991). The use of the

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Modelling Faculty Replacement with Markov Chain 83

stochastic processes, known as Markov processes, has proven useful for human resourceplanning. Faculty planning models that have significant predictive validity can bedeveloped using time-dependent Markov-chain modelling.

The mathematical theory of Markov chains derives from the concepts developed bymathematician A. A. Markov to explain seemingly random, or stochastic, processes.Probability theory, or the theory of stochastic processes, can be thought of as the studyof mathematical models of random events. This math has proven useful in studying largecomplex phenomena with multiple, seemingly independent variables (Wyer, 1988). AMarkov chain can be used as a mathematical model to describe a process that moves ina sequence of steps through a set of states. Markov models are often used to investigatethe current movement of some variable in order to predict the future movement of thatsame variable.

Markov analysis is widely used in business and industry (Becht & Maki, 1987) and themilitary (Gass et at, 1988; Weigel & Wilcox, 1993) to forecast future personnel needs andanalyse potential personnel policy decisions. The literature of educational administrationand planning has shown evidence of some use of Markov processes in areas such asquantifying faculty mobility (Greenberg & McCall, 1983), developing a reduction in forcepolicy (Feldt, 1986) and modelling minority representation policies (Baker & Williams,1986). This widely used and valuable tool should be explored for its applicability tocontemporary staffing dilemmas facing higher education. This study uses a time-depen-dent Markov chain process to predict the future staffing needs of a college of veterinarymedicine within a research university.

The basis of a Markov-chain faculty-planning model is a matrix where each row andcolumn corresponds to a current faculty state such as tenure status, gender, age,retirement, resignation or death. As this is a time-dependent model, faculty movementscan be projected from year to year. In the matrix, the coefficients define the probabilitythat faculty members will move to a different state. The sample in each state must belarge enough to avoid violating a primary assumption of Markov-chain models thattransition probabilities for a state remain constant over time. For planning purposes,however, the transition probabilities can be adjusted to represent changing universitypolices and practices or external conditions such as enrolment demand.

Methods

Data for faculty in the College of Veterinary Medicine at Auburn University werecollected from academic personnel records for 11 years. The data set for each yearincluded social security number, year of birth, contractual year of employment, currentacademic rank, employment status, status date, appointment date, separation date,reason for leaving without tenure, tenure status, date tenure was granted, and annualsalary. The data set included every tenure-track and tenured faculty member in thecollege from fall 1984 to fall 1994.

The faculty planning model developed for this study was similar to the modelsdeveloped by Bleau (1981), Hopkins and Massey (1981) and Montgomery et al. (1994)and incorporated projections of tenure, academic rank, and corresponding appointmentrates over time, by age. Transition probabilities were averaged over the study's ten years,resulting in a 20 X 20 matrix. The transition probabilities were developed from themovement of each faculty member included in the study into, through or out of a givenstate. The 20 states used are detailed in Table 1. The faculty-planning model used theactual distribution of faculty for school year 1994-1995 as a beginning and developed

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84 E. R. Hackett et al.

TABLE 1. Academic staff employment status/age and corresponding states usedto create transitional probabilities

Assistant professor age 26-35 Professor age 36-45Assistant professor age 36-45 Professor age 46-55Assistant professor age 46-55 Professor age 56-65Assistant professor age 56-65 Professor age 66-75Assistant professor age 66-75 Failure to attain tenureAssociate professor age 26-35 Acceptance of other employmentAssociate professor age 36-45 Voluntary separation GTAAssociate professor age 46-55 Voluntary separation healthAssociate professor age 56-65 RetirementAssociate professor age 66-75 Death

projections using the transition probability matrix either as is or adjusted for possiblepersonnel policy changes. The model was programmed using Microsoft Excel (1995)software and implemented as a finite Markov chain.

A finite Markov chain encompasses a finite number of states with the transition matrixdefining the probability that an object will stay in a state or move to another. The entriesin the transition matrix, in this case developed from historical data, represent acombination of employment status and age, are non-negative, and each row has a sumof 1. Starting the Markov process requires a transition matrix and a starting state foreach object, in this case an academic staff appointment and age. Iterative matrixoperations are basic to a Markov chain model (McNamara, 1974). In this case, forexample, a row vector whose components define the probability of being in various statesat a given time was multiplied by the transition matrix and the new product used eachtime in one often iterations. The transition probability matrix, Table 2, details the actualprobabilities of remaining in a state based on the historical data used for this study.

Three alternative scenarios for faculty change over the ten-year period from schoolyear 1994-1995 to 2004-2005 were developed. The first scenario assumed that thetransition probabilities developed from the actual data of the previous ten years wouldhold. The second scenario assumed a hiring freeze for school years 1995-1996 and1996-1997, as could be the case with budgetary restrictions. In this model all transitionprobabilities would remain the same except that there would be no new entries into thematrix for two years. The third scenario assumed that all transition probabilities wouldremain the same except for a 10% increase in retirement in the school years 1995-1996and 2000-2001. This last scenario might be the case if the university offered an earlyretirement option twice in a decade as a means of bringing the average age of the faculty,and so payroll, down.

Results

Ideally, the predictive validity of this model would be calculated with actual faculty datafrom fall 1995 to fall 2004. At the time of preparation of this paper, fall faculty countswere only available for fall 1994 and fall 1995. To test the predictive validity of themodel a transition matrix was created with the first ten years and fall 1994 and fall 1995predicted. A chi-square analysis of observed fall 1994 versus predicted fall 1994 andobserved fall 1995 versus predicted fall 1995 for faculty age and rank distributionsshowed no difference (p > 0.99).

The results of faculty-staffing projections under the three policy scenarios indicate that

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Modelling Faculty Replacement with Markov Chain 85

TABLE 2. Transition probability matrix developed from historical academic staff records for school years1984-1994

Assist 26-35

Assist 36-45

Assist 46-55

Assist 56-65

Assist 66-75

Assoc. 26-35

Assoc. 36-45

Assoc. 46-55

Assoc. 56-65

Assoc. 66-75

Prof. 36-45

Prof. 46-55

Prof. 56-65

Prof. 66-75

Fail Attain Tenure

Other Employ

Vol. Separ. GTA

Vol. Separ. Health

Retirement

Death

Assistant Professor26-35 36-45 46-55 56-65 66-75

0.2292 0.3750

0.5782 0.0295

0.4500 0.1000

0.2750 0.1500

Associate Professor26-35 36-45

0.1 111

0.2396

0.1121

0.5556

0.4908

46-55 56-65

0.1416

0.175

0.3333

0.2706

0.5090

0.1750

0.1250

0.2754

0.3000

66-75

0.0750

0.2500

0.1000

Assist 26-35

Assist 36-45

Assist 46-55

Assist 56-65

Assist. 66-75

Assoc. 26-35

Assoc. 36-45

Assoc. 46-55

Assoc. 56-65

Assoc. 66-75

Prof. 36-45

Prof. 46-55

Prof. 56-65

Prof. 66-75

Fail Attain Tenure

Other Employ

Vol. Separ. GTA

Vol. Separ. Health

Retirement

Death

36-15

0.0313

0.0118

0.0734

0.6364

Professsor

46-55 56-65

0.0295

0.0642

0.0719

0.3636

0.6329

0.0250

0.1257

0.2000

0.3544

0.5905

66-75

0.1422

0.4286

Fail Attain

Tenure

0.0367

1

Accept OtherEmploy.

0.0521

0.0324

0.0138

0.0127

1

VoluntarySeparation

GTA

0.0313

0.0649

0.075

0.0505

0.2500

0.4500

0.0474

0.1071

1

VoluntarySeparation

Health

0.0417

1

Retirement

0.3750

0.0180

0.4500

0.1810

0.4643

1

Death

0.0388

1

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FIG. 1. Faculty by rank actual 1984 and 1994 with 2004 projected based on historical transitional probabilities.

even modest changes in personnel policy can have an appreciable impact on the mix offaculty by age and rank. Figure 1 depicts the faculty by rank and age group at thebeginning and end of the decade used to create the transition matrix and as predictedten years into the future. If recent patterns of faculty change occur, this model would leadto an increase in the ranks of associate professor and a decrease at the assistant and fullprofessor level. As can be seen in Fig. 2 this would also lead to an increase in facultybetween the ages of 46 and 65 in real terms and proportionately. Tables 3 and 4 displaya slight increase in total faculty. This iteration of the Markov-based model begins withthe actual academic staff in financial year (FY) 1994-1995 and depicts a ten-year futurein which changes in the status of personnel occur with a probability defined from theactual changes that occurred in the previous ten-year period. Of course this assumes thatthe pattern of revenue and expense the college would realise during the ten yearsprojected would begin at the base year FY 1994-1995, and recapitulate the previousdecade.

Prediction models cannot be validated until the predicted future arrives. On visualinspection this base model seems reasonable. A faculty with recent significant retirementat the full professor level, and replacement at the assistant professor level, ages and movesup in rank over the ten-year period. The base model includes a 9% increase in facultysize, which mirrors the growth in faculty over the previous decade. This increase of about1% a year can be seen in Table 3, numerical projections by rank, and in Table 4,numerical projections by age.

The second scenario keeps the assumptions in the transition matrix but allows no new

86 E. R. Hackett et al.

55% -•

48.6%

50%. ^flSf^H

sMMM ^ H ^ l 37.8%WM 35.7% ^^^^B ^ ^ ^ ^ H

-fc1 ^ n .^^^^^^^H 32.9% ^^^^^1*3 qso/n ^ n ^ ^ • ^ ^ • ^ H _^^^^^H 31.8%

*° 30%" I 2 6 ' s % 27'12t^^^Hl H 9 |

20%- ^^^^BHHI ^ ^ ^ ^ ^ K ^ I ^^^^^1^115%" ^^^^^1 ^H^B^I ^H^B^Iio%~ ^ H H ^ H I I ^HBI

Assistant Associate ProfessorProfessor Professor

Academic Rank

• 1984 «1994 B2004

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FIG. 2. Faculty by age actual 1984 and 1994 with 2004 projected based on historical transitional probabilities.

faculty to enter the equation during the first two years of the model, simulating a hiringfreeze for the two years FY 1995-1996 and 1996-1997. This model, as seen in Fig. 3,would lead to an increase at the level of associate and full professor and a significant drop

TABLE 3. Academic staff by rank for school years 1984 and 1994 actual and 2004 projected

Forecast based on transitional probabilities alone

Assistant professorAssociate professorProfessor

Total

Forecast including simulation of a hiring freeze in

Assistant professorAssociate professorProfessor

Total

1984

34232885

%

40.027.132.9

100

the first two years

34232885

40.027.132.9

100

1994

26353798

26353798

Forecast including simulation of an early retirement option in years one and five

Assistant professorAssociate professorProfessor

Total

34232885

40.027.132.9

100

26353798

26.5 .35.737.8

100

26.535.737.8

100

26.535.737.8

100

2004

215234

107

12434095

305323

106

%

19.648.631.8

100

12.645.342.1

100

28.350.021.7

100

Modelling Faculty Replacement with Markov Chain 87

45%-

37.6%40%-

S*®iiB 35-7%H ^ ^ - ^ _ 35.5%H^^^^H 33.6%35%- H H H 32.7°/<y—

^•^^1 ^ • H 28.0%

30%- H H H 2 8 ' 2 i i H H H Ofi so/

rt 25%- ^ ^ B B HHH1 >rHHH

S 20%- ^^11 I^H ^^Hl° ^H^lH ^H^BH ^ • • H< ^^H^^R^^I ^^^^^H^^l ^^^^^H^^lu ^^^^^H ^H^B^I ^^B^^H

pin ^^^^^^^^B ^^^H^^^^H ^^^B^H^^I

15%- ^•H ^HII ^ Bl4.7% ^ H H ^^H ^ ^ 1 4.1%

5%- fMM !.0% • • • ^ H l H I I S M I'9%

26-35 36-45 46-55 56-65 66 6s Over

Age Class

D1984 B1994 «2004

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88 E. R. Hackett et al.

TABLE 4. Academic staff by age for school years 1984 and 1994 actual and 2004 projected

1984

Forecast based on transitional probabilities alone

Age 26-35Age 36-45Age 46-55Age 56-65Age 65 and over

Total

43224205

85

%

4.737.628.223.55.9

100

Forecast including simulation of a hiring freeze in the first two years

Age 26-35Age 36-45Age 46-55Age 56-65Age 65 and over

Total

Forecast including simulation of an ear

Age 26-35Age 36-45Age 46-55Age 56-65Age 65 and over

Total

43224205

85

4.737.628.223.55.9

100

1994

13532264

98

13532264

98

ly retirement option in years one and five

43224205

85

4.737.628.223.55.9

100

13532264

98

%

1.035.732.726.54.1

100

1.035.732.726.54.1

100

1.035.732.726.54.1

100

2004

13836302

107

03134264

95

14348131

106

%

0.935.533.628.0

1.9100

032.635.827.44.2

100

0.940.645.312.30.9

100

at the rank of assistant professor. Figure 4 indicates that, like the base model, facultybetween the ages of 46 and 65 would increase in real terms and proportionately; Tables3 and 4 display a slight decrease in the overall number of faculty for this model of ahiring freeze. The university whose data were being used to test this analytical strategyis located in a state where the incoming governor was implementing a hiring freeze atthe time of this analysis, giving this particular model a certain relevancy.

This second iteration of the Markov-chain forecast begins to show the differencebetween a simple cohort analysis by rank and an analysis that provides for different stateswithin a rank cohort and discrete probabilities within each state. The increase in thenumber and percentage at the full professor level is counterintuitive from a cohortanalysis perspective. For this study the investigators chose a finite Markov-chainmodelling strategy with its assumption that entries in the transition matrix are non-negative and that each row has a sum of 1. By definition, information will be lost to themodel in the withholding of data for the first two iterations at the beginning academicstaff level. Given the assumption that each row has a sum of 1, the information will beregained for the other states and iterations. In other words, shifting between all the otherpossible iterations of academic staff by age, rank, and employment status will occurfollowing probabilities based on a history of the previous behavior of the college. Thecollege itself represents a programme of work that must be accomplished and a complexset of interrelations between policy, positions, and those that accomplish the work. Givenpast behaviour, this model predicts that disruption of previous patterns, provided bywithholding entry-level positions, will place 10% more activity at the rank of fullprofessor than would otherwise have been forecast. In other words, more associateprofessors will be retained and persist at the college and move to full professor. In thesame projection fewer assistant professors will lead to a smaller pool of associateprofessors.

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Modelling Faculty Replacement with Markov Chain 89

FlO. 3. Faculty by rank actual 1984 and 1994 with 2004 projected based on historical transitional probabilitiesadjusted to simulate a hiring freeze for the first two years of the projection.

The third scenario, again, keeps all the base assumptions inherent in the transitionmatrix except one. This model assumes a 10% increase in faculty retirements in the firstand fifth years, simulating the offering of an early retirement option in both of thoseyears. This model, as seen in Fig. 5, would lead to an increase at the rank of associateprofessor, as in the base model, with a substantial drop at the rank of full professor.Unlike the other two models this assumption would lead to a proportionate increase atthe rank of assistant professor for fall 2004. Figure 6 details the move of the faculty ageprofile with this policy toward the 36—45 and 46—55 age groups with an increase in theoverall number of faculty. As with the second model, given the assumption that each rowhas a sum of 1, information will be regained within the context of the other states anditerations. Given past behaviour, this model predicts that disruption of previous patterns,provided by the accelerated retirement of full professors, will place more activity at therank of assistant and associate professor than would otherwise have been forecast. Inother words, more assistant professors will be hired, retained and will persist at thecollege and move to associate professor.

Discussion

Reviewed as a whole, the results of the three different models suggest that some actionmust be taken if the faculty is to remain balanced between ranks and not significantlyadding to budgetary pressure. If current trends continue, this faculty will increase in age,

50%-. 45.3%

45%- 40.0% fiBS JIM

40%- ^—\\ 35.7%[ BM J | lI . ^ H ^ B I 32.9% ^ H ^ E H

3 30%. j ~6'5% 2 7 ' 1 ° " ° ^ | H HHII UH / ! • • • • « •*° 25%" ^^^1 ^ H ^ B I ^ I ^ B Is 20%- ^^^| ^ • ^ • 1 ^ • ^ • 1^ ^^^1 12.6% ^ H ^ K I ^ H ^ B I

15%- ^^H^n ^ H ^ B H ^I^BH

IO%- ^H^B^I ^ H ^ B I ^IIBll

Assistant Associate ProfessorProfessor Professor

Academic Rank

• 1984 B1994 B2004

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rank and size, so increasing the personnel expense demands on the overall budget. Ahiring freeze would keep the faculty near the same size but push more faculty into higherranks. An early retirement option would create a younger overall faculty with an increasein the ranks of assistant professors and an increase in faculty size based on past hiringand retention strategies. This investigation suggests that some combination of an earlyretirement option and a hiring freeze would keep an appropriate mix between age, rankand size of faculty. These results are not startling. However, even this fairly straightfor-ward study suggests that the dynamics of faculty retention and mix are complex. Theinvestment in an appropriate analytical strategy can provide additional uncertainty-reducing information to decision makers. Patterns of personnel retention and separationare not usually projected. Instead, anecdote and myth are used during the discussion ofpolicy options such as those modelled in the current study.

The primary expense in the delivery of higher education is faculty salary. For thatreason alone, it is essential to understand the potential behaviour of the key characteris-tics of the faculty when planning for the immediate five to ten year future. Policydecisions on hiring have a substantial impact on future budgets and so on campusfinancial flexibility. Not only is faculty size a consideration in fiscal planning but also themix of faculty by rank and age. For the institution under study, and higher education asa whole, the trend has been toward an older, more senior faculty. The fiscal implicationsare clear. Over and above fiscal considerations, the optimal mix of faculty by age andrank to assure both innovation and stability must be attended to. Both fiscal concernsand faculty composition concerns should be addressed using models such as thosedemonstrated in this study. Markov-chain modelling can be a useful tool in estimatingthe impact of faculty hiring, promotion and separation strategies. At interest is the ability

90 E. R. Hackett et al.

45%-i

40%- 37.6%> ^ M 35.7% 35.8%

35%- |^^B32.6% 32.7%^HjH

30%- ^ i H 28%^HHI 27.4%

" 2o%" iH ^H III15%- ^BII ^BII IBII O ' ! / ° " ^•^•fl ^H iB H I coot

^^^•^^•^^H ^^^•^^•^H ^^^^^^^^H ^ iiy

26-35 36-45 46-55 56-65 66 & OverAge Class

nl984 »1994 S2004

FIG. 4. Faculty by age actual 1984 and 1994 with 2004 projected based on historical transitional probabilitiesadjusted to simulate a hiring freeze for the first two years of the projection.

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Modelling Faculty Replacement with Markov Chain 91

FIG. 5. Faculty by rank actual 1984 and 1994 with 2004 projected based on historical transitional probabilitiesadjusted to simulate an early retirement incentive for the first and fifth year of of the projection.

to understand and predict faculty appointment, tenure, and age distribution. As amodelling tool, the transition probabilities can be used to project different forward yearsand to represent changing external conditions or institutional policy.

This study was limited in that it focused on a college within the university which usesfew short-term renewable contract faculty. The strength of Markov-chain analysis is itsability to take multi-state historical data and predict future states. A limit of thismodelling strategy is including multiple or complex policy changes in predicting futurestates. Each manipulation, based on some personnel policy change applied in the future,requires developing a mathematical complement to the assumed policy. In the currentstudy the potential policy shifts explored were fairly simple. Historical data, whereavailable, provide a most acceptable guide to developing manipulations for modellingpurposes.

Given the results of the current investigation the institution under study has chosen todevelop a Markov-chain modelling capability for all personnel needs. The projected fiveto ten year economic future for the state within which this institution is a constitutionalentity would lead to the assumption that increases in funding will not be routine.Programmatic demands from the institution's service area are changing. Even mode ofdelivery, whether on campus or at a distance from the main campus, is under discussion.These forces are at work throughout higher education. Planning for the future will

55%-i50.0%

45%- S^H^^I40.0% ^^B^H

>• ' "/A B^H^H 37.8%40%- |^-—g|l 35.7%[^Hj^H ^ ^ ^ M

& Ull .^^H^^H^^I TO QOA ^^^^^^ |

fc | |a 28.3% ^ ^ • ^ H ^ H ^ ^ ^ ^ |^ ,™ Wl2G.a% 27 .1%^H^H^1 ^ ^ ^ H

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20%" ^ H ^ s l ^HH[^1 ^Hfli^P

10%" ^H^KI ^ H K I ^•^B^lAssistant Associate ProfessorProfessor Professor

Academic Rank

• 1984 B1994 E2004

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FIG. 6. Faculty by age actual 1984 and 1994 with 2004 projected based on historical transitional probabilities.

require a more sophisticated understanding of the movement of faculty into, through,and out of the institution.

Correspondence: Ray Hackett, 4032 Haley Center, Auburn University, Auburn, AL 36849,USA. Tel: + 1 334 844 3082; Fax: + 1 334 844 3072; E-mail: hack-era@mail.auburn.edu.

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92 E. R. Hackett et al.

SO%-i45.3%

45%- ^S»fl40.6% HI

36%^BH ^ B H40%- 37.6% • • H |

35%- J i l l 3 2 < 7 ° - ^ H H

~B 3 0 % - • • • i f lH 26.5%

s 20%- B ^ B I B ^ H I B H

io%~ B l l H^KI H ^ H

s%- fSM o°-9°' I I I K I • • B r Kio9°/

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Modelling Faculty Replacement with Markov Chain 93

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