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Short-term enrollment projection: an example at state level.

With information obtained from reviews of past enrollment trends, it is both natural and logical that a researcher make an assessment of future enrollment. Enrollment projections are imperative if we are to allocate resources judiciously. The uncertainty that accompanies our move towards the next millennium further augments the need for accurate projections. In order for these projections to be thorough, it is necessary to carefully examine not only the social and political factors that affect studies as a whole, but also, the specific dynamics within different types of enrollment studies.

Factors that significantly affect enrollment are numerous and diverse. Chief among these factors is the pervasive uncertainty to the prospect of college enrollment provided by both the national and local economy pictures. The inversely proportional relationship between the employment rate and the enrollment rate is widely accepted despite the elusive nature of the exact length of the business cycle itself that results in the uncertainty of projections of future college enrollment. Tax policy, another aspect of both local and national economies, also plays a major role in influencing access to higher education, and therefore enrollment. For example, the passage of a bill that allows for tax breaks of those families supporting a college student would likely result in a significant increase in enrollment. In fact, the availability of student aid has been determined as a correlate of enrollment change. In the sphere of higher education, financial aid is an indispensable tool of student recruitment. This particular source of funding is the reason that, at the aggregate level, enrollment tends to increase while at a particular campus, the enrollment may be decreasing. The additional financial aid at: private institutions helps to offset the edge of low tuition policy enjoyed by the public institutions.

Other major factors not linked directly to the economy include birth rates and interstate migration. Increase in the age cohort of 18-24 increase the enrollment of the class of first time freshmen, while increase in the age cohort of 25-30 tends to boost the enrollment of the adult learner group. Change in the structure of industry is also a major factor in that it affects population size. The net change in terms of state migration determines whether or not there is an increase in college enrollment. Other less tangible, but equally influential factors include the socio-economic status of the prospective student's family, peer influence and the quality of the prospective student's secondary education. It is a widely-accepted notion that high school graduates from middle class families are more likely to enroll in college than their counterparts from working class families. Peer influence also has a high correlate with the student's aspiration for higher education.

There are two fundamental types of problems that must be addressed in enrollment analysis--interstate and intrastate migration. However, the impact of these two issues on any enrollment analysis is dependent on the focus of the analysis. If the focus of the analysis is the aggregate level, the significance of migration is reduced, while enrollment analysis on the institutional level reinforces the impact of migration. The choice of students to attend a specific institution when close substitutes are available is a major concern of the individual institution, but does not affect the enrollment at the state level. Parallel to the first problem is the in-state migration of transfer students. The question of how to define the sample of potential transfer students is a major task facing researchers at individual institutions. This category is defined by those students who can transfer back and forth between four year institutions or between community colleges and four year institutions. However, each type of the different potential clientele has specific needs and characteristics. This difficulty is greatly reduced when enrollment estimation is made at the state level and students can only transfer between public institutions. Even the model of state level enrollment estimation is small, relying only on past enrollment data and ignoring certain potentially influential enrollment.

The techniques of enrollment forecasting, which have been well discussed by Wang (Wang, 1974), reflect the intricacies of the enrollment trend. The methods of simple averages, moving averages, exponential smoothing, exponential models, system equation, Markov transition model, path analysis and ratio methods have been used in predicting enrollment of higher education. As a result of the complexity of the enrollment projection, it is highly unlikely that any single technique is entirely appropriate to all enrollment analyses. A curve-fitting technique such as regression analysis, which was widely used throughout the period of increasing enrollment overstates the enrollment at the present time. An average method may provide a quick estimation when the enrollment trend become stable. Exponential smoothing is too subjective, since the large values of alpha are too vulnerable to recent changes (Gardner, 1981). The ratio method is only appropriate when an institution shares a large percentage of an available student pool.

Time-series analysis developed by Box and Jenkins, has garnered wide reception in enrollment forecasting. This method is superior to simple regression analysis in that the problem of autoregression is excluded in the time-series analysis. As software such as SAS and SPSS have included time-series analysis in the packages, the complicated computations become less formidable. The few data elements required in using this technique also make this method of forecasting more appealing.

The box-jenkins model includes several major steps. Historical data is used to identify a model and its parameters. Various diagnostics are used to check the accuracy of the model and to propose a new improved model. And finally the chosen model is used for forecasting time series values. The chosen model is an ARIMA model (1,2,2) of which the behavior of the sample autocorrelation function (SAC) and the sample partial autocorrelation function (SPAC) has been examined. Taking second differences of the original time series and using log transformation, the ARIMA model (p,d,q) was identified with parameters p equals to 1, and q equals to 2. With all these parameters, time series values have been forecasted as presented in table 2.

Table 2 Box-Jenkins Var=Enrl/Plot=Ser/Log/Difference=2/P=2/Q=2/ Identify/Origin=-9/Forecast
Forecast Error Summary Table In Transformed Units

         Forecast      Forecast      Impulse
Lead     Variance        S.E.       Resp Func

1       0.43519E-04   0.65969E-02    1.2578
2       0.11237E-03   0.10600E-01    4.3019
3       0.91776E-03   0.30294E-01   10.195
4       0.54406E-02   0.73760E-01   16.366
5       0.17097E-01   0.13075       20.650
6       0.35655E-01   0.18882       23.173
7       0.59024E-01   0.24295       25.644
8       0.87642E-01   0.29604       29.382
9       0.12521       0.35385       34.202
10      0.17612       0.41966       38.974
11      0.24222       0.49216       42.901
12      0.32232       0.56773

Forecasts At Increasing Lead For Variable Enrl
Starting Origin At 5

Lead Time                      1             2

OBS             Data

5            2.00117E+05
6            2.04344E+05   2.03402E+05
7            2.02647E+05   2.02534E+05   1.99449E+05
8            1.96934E+05   1.96828E+05   1.96691E+05
9            1.91859E+05   1.91920E+05   1.90033E+05
10           1.89993E+05   1.89958E+05   1.90033E+05
11                         1.89341E+05   1.89287E+05
12                                       1.86849E+05

Lead Time        3              4             5


8            1.92488E+05
9            1.89595E+05   1.87616E+05
10           1.89595E+05   1.88524E+05   1.85872E+05
11           1.89556E+05   1.88520E+05   1.86814E+05 1.8
12           1.86699E+05   1.87305E+05   1.85665E+05 1.8

Discussion: The projected enrollment figure for 1997 is 268, 159 which is slightly below the figure 173,379 in 1996. This model looks very reasonable when one compare the projected figures (from 1991 to 1996) to the actual enrollment figures. The enrollment trend seems to move downward as the data indicated.

As indicated in the literature of higher education, the accuracy of the model lies in the basic assumptions of the model. If the assumptions are incorrect, the complicated mathematical computation is invalid for this particular study.

Conclusion: Needless to say, enrollment projection is very difficult to perform. Any factors outside the model that are subject to change will most likely exert great impact on enrollment. Effort by the institutions outside the state could greatly influence the matriculation rate of incoming freshmen. This is the reason why continued updating of the enrollment model becomes essential to the yearly planning and budgeting cycle yearly. Reviewing the basic assumptions of the projection model, along with external factors, is the best strategy in dealing with the fluctuations of enrollment.



Box, G.E.P. and G.M. Jenkins, Time Series Analysis: Forecasting and Control. San Francisco: Golden-Day, 1976.

Gardner, E.D., "Weighting Factor Selection in Double Exponential Smoothing Enrollment Forecasts. "Research in Higher Education, 14 (1981), 49-56.

Missouri Higher Education, 1995-1996 statistic summary. Missouri Coordinating Board for Higher Education, July 1996

Wing, P. Higher Education Enrollment Forecasting: A Manual for State Level Agencies. Boulder, Colorado: National Center for Higher Education Management Systems, 1974.

"Forecasting Enrollment and Student Demographic Conditions." in Tedamus, P. and M.W. Peterson and Assoc., eds., Improving Academic Management-A Handbook of Planning and Institutional Research. San Francisco: Jossey-Bass, 1980.
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Title Annotation:Teacher Assessment
Author:Liu, Richard
Date:Jun 22, 1998
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