Projections of Education Statistics to 2011: Appendix A1 Enrollment

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A1. Enrollment

National

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.

Education Forecasting Model

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) full-time college enrollment, and (2) part-time college enrollment. Within an enrollment category, where applicable, enrollment rates were projected by individual ages 16 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 1999. Different assumptions were made to produce low, middle, and high alternative projections of enrollment rates to the year 2011.

College Full-Time and Part-Time Enrollment

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 economic assumptions. Table A1.1 shows enrollment rates for 1999 and middle alternative projected enrollment rates for 2006 and 2011. Table A1.2 shows the equations used to project enrollment rates for men by attendance status. Table A1.3 shows the equations used to project enrollment rates for women by attendance status.

Enrollment in Public Elementary and Secondary Schools, by Grade Group and Organizational Level

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 progression rate projections were used for grades 2 through 12. Table A1.4 shows the public school enrollment rates and table A1.5 shows the public school grade progression rates for 1999 and projections for 2006 and 2011. The projected rates in tables A1.4 and A1.5 were used to compute the projections of enrollments in elementary and secondary schools, by grade, shown in table 1.

College Enrollment, by Sex, Attendance Status, and Level Enrolled; and by Type and Control of Institution

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 2006 and 2011 are shown in tables A1.6 and A1.7, along with actual values for 1999. For all projections, it was assumed that there was no enrollment in 2-year institutions at the postbac-calaureate level (graduate and first-professional).

The projected rates in tables A1.6 and A1.7 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 2006 and 2011 are shown in table A1.8, along with actual percents for 1999. 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 1999 and projections for 2006 and 2011 are shown in table A1.9. The projected rates in table A1.9 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.

Full-Time-Equivalent Enrollment, by Type and Control of Institution and by Level Enrolled

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 1999 and projections for 2006 and 2011 are shown in table A1.10.

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.

Projection Accuracy

An analysis of projection errors from the past 18 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 0.2, 0.5, 1.2, and 2.9 percent, respectively. For the 1-year-out prediction, this means that one would expect the projection to be within 0.2 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 0.3, 0.5, 1.2, and 4.3 percent, respectively, while those for projections of public school enrollment in grades 9-12 were 0.4, 0.7, 1.3, and 2.6 percent for the same lead times.

For projections of total enrollment in degree-granting institutions, an analysis of projection errors based on the past 6 editions of Projections of Education Statistics indicates that the MAPEs for lead times of 1, 2, and 5 years were 1.0, 0,9, and 2.2 percent, respectively. For the 1-year-out prediction, this means that one would expect the projection to be within 1.0 percent of the actual value, on the average. For more information on mean absolute percentage errors, see table A2.

Basic Methodology

The notation and equations that follow describe the basic models used to project public elementary and secondary enrollment.

Public Elementary and Secondary Enrollment

Let:

i = Subscript denoting age

j = Subscript denoting grade

t = Subscript denoting time

K_t = Enrollment at the nursery and kindergarten level

G_jt = Enrollment in grade j

G_1t = Enrollment in grade 1

E_t = Enrollment in elementary special and ungraded programs

S_t = Enrollment in secondary special and ungraded programs

PG_t = Enrollment in postgraduate programs

P_it = Population age i

RK_t = Enrollment rate for nursery and kindergarten

RG_1t = Enrollment rate for grade 1

RE_t = Enrollment rate for elementary special and ungraded programs

RS_t = Enrollment rate for secondary special and ungraded programs

RPG_t = Enrollment rate for postgraduate programs

EG_t = Total enrollment in elementary grades (K-8)

SG_t = Total enrollment in secondary grades (9-12)

R_jt = Progression 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:

formula 5

Higher Education Enrollment

For institutions of higher education, projections were computed separately by sex and attendance status of student. The notation and equations are:

Let:

i = Subscript denoting age except:

i = 25: ages 25-29

i = 26: ages 30-34

i = 27: ages 35 and over for enrollment (35-44 for population)

t = Subscript denoting year

E_it = Enrollment of students age i

P_it = Population age i

R_it = Enrollment rate for students age i

T_it = Total enrollment for particular subset of students: full-time men, full-time women, part-time men, part-time women

Then:

Where:

Methodological Tables

Tables A1.11 and A1.12 give the rates used to calculate projections of enrollments and basic assumptions underlying enrollment projections.

Private School Enrollment

This edition is the first report that contains projected trends in elementary and secondary enrollment by grade level in private schools produced using the grade progression rate method.

Private school enrollment data from the National Center for Education Statistics' Private School Universe Survey for 1989-90, 1991-92, 1993-94, 1995-96, 1997-98, and 1999-2000 were used to develop these projections. In addition, population estimates for 1989 to 1999 and population projections for 2000 to 2011 from the U.S. Department of Commerce, Bureau of the Census were used to develop the projections.

The grade progression rate method was used to project private elementary and secondary school enrollment. The grade progression rate method starts with 6-year-olds entering first grade and then follows their progress through private 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.

Projections of enrollment in private elementary and secondary schools were developed using primarily the grade progression rate 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 progression rates. 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 grade progression 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 1999 levels. To obtain projections of total enrollment, projections of enrollments for the individual grades (kindergarten through 12) and ungraded and special classes were summed.

The grade progression rate method assumes that past trends in factors affecting private school enrollments will continue over the projection period. This assumption implies that all factors influencing enrollments will display future patterns consistent with past patterns. This method implicitly includes the net effect of such factors as migration, dropouts, deaths, nonpromotion, and transfers to and from public schools.

Mean absolute percentage errors (MAPEs) of the projection accuracy of private school enrollment were not developed because these projections were prepared for the first time using a new data source and methodology. As additional data becomes available MAPEs can then be calculated.

State-Level

This edition contains projected trends in elementary and secondary enrollment by grade level in public schools from 2000 to the year 2011. This is the seventh 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 1999 were used to develop these projections. This survey does not collect data on enrollment for private schools. In addition, population estimates for 1970 to 1999 and population projections for 2000 to 2011 from the U.S. Department of Commerce, Bureau of the Census were used to develop the projections.

Table A1.11 describes the number of years, projection methods, and smoothing constants used to project enrollments in public schools. Also included in table A1.11 is the procedure for choosing the different smoothing constants for the time series models.

Projections of enrollment in public elementary and secondary schools by state were developed using primarily the grade progression rate 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 progression 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 grade progression 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 1998 levels. To obtain projections of total enrollment, projections of enrollments for the individual grades (kindergarten through 12) and ungraded and special classes were summed.

The grade progression rate method assumes 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.

Adjustment to National Projections

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.