Projections of Education Statistics to 2008 / Appendix A1
Enrollment projections were based on projected enrollment rates, by age and sex, which were applied to population projections by age and sex developed by the Bureau of the Census. These enrollment rates were projected by taking into account the most recent trends, as well as the effects of economic conditions and demographic changes on a person's decision to enter college. The enrollment rates were then used in the Education Forecasting Model (EDMOD), which consists of age-specific rates by sex and by enrollment levels (nursery school through college). The model has 4 stages. See figure 71.
The first stage of EDMOD is an age-specific enrollment model in which enrollment rates are projected and applied to age-specific population projections. This stage, which is used separately for each sex, includes the following categories: (1) nursery and kindergarten, (2) elementary grades 1-8, (3) secondary grades 9-12, (4) full-time college enrollment, and (5) part-time college enrollment. For each of these enrollment categories, enrollment rates were projected by individual ages 3 through 24 and for the age groups 25 to 29, 30 to 34, and 35 years and over.
Enrollments by age and age groups from the Bureau of the Census were adjusted to NCES totals to compute enrollment rates for 1972 through 1995. Different assumptions were made to produce low, middle, and high alternative projections of enrollment rates to the year 2008.
Projections of elementary enrollment rates were considered for ages 5 through 18. Elementary enrollments are negligible for the remaining ages. Because most elementary enrollment rates have been close to 100 percent from 1972 to 1995, alternative enrollment rate projections were not computed. The only set of enrollment rate projections computed was based on the assumption that rates will remain constant through the year 2008 (table A1.1). Several of the rates in table A1.1 exceed 100 percent, as a result of several factors. The enrollment data by age were prorated to agree with NCES totals. The Bureau of the Census does not revise enrollment estimates by age, but population estimates are revised regularly.
Projections of secondary enrollment rates were considered for ages 12 through 34. Secondary enrollments are negligible for the remaining ages. Secondary enrollment rates have fluctuated within a narrow range from 1972 to 1995. Therefore, alternative enrollment rate projections were not calculated. The only set of projections computed was based on constant enrollment rates (table A1.2).
Projections of full-time and part-time college enrollments were considered only for ages 16 and over. College enrollment is negligible for earlier ages. Three alternative projections were made using various assumptions. Table A1.3 shows enrollment rates for 1995 and low, middle, and high alternative projected enrollment rates for 2003 and 2008.
Table A1.4 shows the equations used to project enrollment rates for men by attendance status. Table A1.5 shows the equations used to project enrollment rates for women by attendance status.
The second stage of EDMOD projects public enrollment in elementary and secondary schools by grade group and by organizational level. Public enrollments by age were based on enrollment rate projections for nursery and kindergarten, grade 1, elementary ungraded and special, secondary ungraded and special, and postgraduate enrollment. Grade retention rate projections were used for grades 2 through 12. Table A1.6 shows the public school enrollment rates and table A1.7 shows the public grade-retention rates for 1995 and projections for 2003 and 2008. The projected rates in tables A1.6 and A1.7 were used to compute the projections of enrollments in elementary and secondary schools, by grade, shown in table 1.
The third stage of EDMOD projects enrollments in institutions of higher education, by sex, attendance status, and level enrolled by student and by type and control of institution. For each age group, the percent of total enrollment by age, attendance status, level enrolled, and type of institution was projected. These projections for 2003 and 2008 are shown in tables A1.8 and A1.9, along with actual values for 1995. For all projections, it was assumed that there was no enrollment in 2-year institutions at the postbaccalaureate level (graduate and first-professional).
The projected rates in tables A1.8 and A1.9 were then adjusted to agree with the projected age-specific enrollment rates in the first stage of EDMOD. The adjusted rates were then applied to the projected enrollments by age group, sex, and attendance status from the first stage of EDMOD to obtain projections by age group, sex, attendance status, level enrolled, and type of institution.
For each enrollment category--sex, attendance status, level enrolled, and type of institution--public enrollment was projected as a percent of total enrollment. Projections for 2003 and 2008 are shown in table A1.10, along with actual percents for 1995. The projected rates were then applied to the projected enrollments in each enrollment category to obtain projections by control of institution.
For each category by sex, enrollment level, and type and control of institution, graduate enrollment was projected as a percent of postbaccalaureate enrollment. Actual rates for 1995 and projections for 2003 and 2008 are shown in table A1.11. The projected rates in table A1.11 were then applied to projections of postbaccalaureate enrollment to obtain graduate and first-professional enrollment projections by sex, attendance status, and type and control of institution.
The fourth stage of EDMOD projects full-time-equivalent enrollment, by type and control of institution and by level enrolled. For each enrollment category by level enrolled and by type and control of institution, the full-time-equivalent of part-time enrollment was projected as a percent of part-time enrollment. Actual percents for 1995 and projections for 2003 and 2008 are shown in table A1.12.
These projected percents were applied to projections of enrollment by level enrolled and by type and control of institution from the third stage of EDMOD. The projections were added to projections of full-time enrollment (from the previous stage) to obtain projections of full-time-equivalent enrollment.
An analysis of projection errors from the past 13 editions of Projections of Education Statistics indicates that the mean absolute percentage errors (MAPEs) for lead times of 1, 2, 5, and 10 years out for projections of public school enrollment in grades K-12 were 0.4, 0.6, 1.4, and 2.4 percent, respectively. For the 1-year-out prediction, this means that one would expect the projection to be within 0.4 percent of the actual value, on the average. For projections of public school enrollment in grades K-8, the MAPEs for lead times of 1, 2, 5, and 10 years were 0.5, 0.8, 1.8, and 3.6 percent, respectively, while those for projections of public school enrollment in grades 9-12 were 0.7, 0.7, 1.0, and 3.8 percent for the same lead times.
For projections of enrollment in higher education, an analysis of projection errors based on the past ten editions of Projections of Education Statistics indicates that the MAPEs for lead times of 1, 2, and 5 years were 2.3, 3.4, and 6.7 percent, respectively. For the 1-year-out prediction, this means that one would expect the projection to be within 2.1 percent of the actual value, on the average.
The notation and equations that follow describe the basic models used to project public elementary and secondary enrollment.
i = Subscript denoting age
j = Subscript denoting grade
t = Subscript denoting time
Kt = Enrollment at the nursery and kindergarten level
Gjt = Enrollment in grade j
G1t = Enrollment in grade 1
Et = Enrollment in elementary special and ungraded programs
St = Enrollment in secondary special and ungraded programs
PGt = Enrollment in postgraduate programs in secondary schools
Pit = Population age i
RKt = Enrollment rate for nursery and kindergarten
RG1t = Enrollment rate for grade 1
REt = Enrollment rate for elementary special and ungraded programs
RSt = Enrollment rate for secondary special and ungraded programs
RPGt = Enrollment rate for postgraduate programs
EGt = Total enrollment in elementary grades (K-8)
SGt = Total enrollment in secondary grades (9-12)
Rjt = Retention rate for grade j: the proportion that enrollment in grade j in year t is of enrollment in grade j - 1 in year t-1.
Then:
Where:
Kt = RKt(P5t)
Gjt = Rjt(Gj-1,t-1)
G1t = RG1t(P6t)
PGt = RPGt(P18t)
For institutions of higher education, projections were computed separately by sex and attendance status of student. The notation and equations are:
i = Subscript denoting age except:
t = Subscript denoting year
Eit = Enrollment of students age i
Pit = Population age i
Rit = Enrollment rate for students age i
Tit = Total enrollment for particular subset of students: full-time men, full-time women, part-time men, part-time women
Then:
Where:
Eit = Rit(Pit)
The tables in this section give the rates used to calculate projections of enrollments, basic assumptions underlying enrollment projections (table A1.13), and methods used to estimate values for which data are not available (table A1.14).
Projections of private school enrollment were derived in the following manner. From 1970 to 1995, the ratio of private school enrollment to public school enrollment was calculated by grade level. These ratios were projected using single exponential smoothing, yielding a constant value over the projection period. This constant was then applied to projections of public school enrollment by grade level to yield projections of private school enrollment. This method assumes that the future pattern in the trend of private school enrollment will be the same as that in public school enrollment. The reader is cautioned that a number of factors could alter the assumption of a constant ratio over the projection period.
This edition contains projected trends in elementary and secondary enrollment by grade level in public schools from 1997 to the year 2008. This is the sixth report on state-level projections for public school elementary and secondary education statistics.
Public school enrollment data from the National Center for Education Statistics' Common Core of Data survey for 1970 to 1995 were used to develop these projections. This survey does not collect data on enrollment for private schools. In addition, population estimates for 1970 to 1996 and population projections for 1997 to 2008 from the U.S. Department of Commerce, Bureau of the Census were used to develop the projections.
Table A1.15 describes the number of years, projection methods, and smoothing constants used to project enrollments in public schools. Also included in table A1.15 is the procedure for choosing the different smoothing constants for the time series models.
The grade retention method and the enrollment rate method were used together to project public elementary and secondary school enrollment by state. The grade retention method starts with 6-year-olds entering first grade and then follows their progress through public elementary and secondary schools. The method requires calculating the ratio of the number of children in one year who "survive" the year and enroll in the next grade the following year. The enrollment rate method expresses the enrollment of a particular age group as a percent of the population for the same age group. The projections produced from these two methods were combined to yield a composite projection of enrollment.
First, projections of enrollment in public elementary and secondary schools by state were developed using primarily the grade retention method. Kindergarten and first grade enrollments are based on projected enrollment rates of 5- and 6-year-olds. These projected enrollment rates are applied to population projections of 5- and 6-year-olds developed by the Bureau of the Census.
Enrollments in grades 2 through 12 are based on projected grade retention rates in each state. These projected rates are then applied to the current enrollment by grade to yield grade-by-grade projections for future years. Enrollment rates of 5- and 6-year-olds and retention rates are projected using single exponential smoothing. Elementary ungraded and special enrollments and secondary ungraded and special enrollments are projected to remain constant at their 1995 levels. To obtain projections of total enrollment, projections of enrollments for the individual grades (kindergarten through 12) and ungraded and special classes were summed.
Second, projections of enrollments in public elementary and secondary schools by state were developed using the enrollment rate method. Enrollment in grades K-8 was expressed as a percent of the 5- to 13-year-old population for 1970 to 1995. Similarly, enrollment in grades 9-12 was expressed as a percent of the 14- to 17-year-old population. These percents were then projected using single exponential smoothing and applied to projections of the 5- to 13-year-old and 14- to 17-year-old populations developed by the Bureau of the Census.
The enrollment rate and grade retention methods assume that past trends in factors affecting public school enrollments will continue over the projection period. This assumption implies that all factors influencing enrollments will display future patterns consistent with past patterns. Therefore, this method has limitations when applied to states with unusual changes in migration rates. This method implicitly includes the net effect of such factors as migration, dropouts, deaths, nonpromotion, and transfers to and from private schools.
Projections of state public school enrollment are based on the grade retention and enrollment rate methods. Empirical research on national models suggests that the enrollment rate method is superior to the grade retention method as the lead time of the projection increases. For longer lead times, the mean absolute percentage errors of the projections of national public school enrollment based on the enrollment rate method are smaller than those based on the grade retention method. It is reasoned that because the projections based on the enrollment rate method depend on population projections, they reflect long-term shifts in state migration patterns as projected by the Bureau of the Census. On the other hand, the projections based on the grade retention method reflect the net effects of state in- and out-migration for the short term.
For a particular year, the projections of enrollments developed using the grade retention and enrollment rate methods were combined using a simple linear combination of the projections as follows:
E = bX1 + (1-b)X2
E = combined enrollment projection
X1 = projection based on the grade retention rate
X2 = projection based on the enrollment rate method
b = weight
Here, b is an adaptive parameter that changes in time to give the most weight for longer lead times to the most successful of the two projection methods, the enrollment rate. Table A1.16 presents the weights used to combine the two methods. The sum of the weights b and 1-b is constrained to sum to 1.
The sum of the projections of state enrollments was adjusted to equal the national projections of public school K-12, K-8, and 9-12 enrollments shown in table 1. For details on the methods used to develop the national projections for this statistic, see the section on national enrollment projections in this appendix.
