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Projections of Education Statistics to 2014, published September 2005.

Appendix A. Projection Methodology: Enrollment

National

Enrollment projections are based on projected enrollment rates, by age and sex, where the enrollment rate for a given population for a certain level of education is the number of people in that population enrolled at that level of education divided by the total number of people in that population. These enrollment rates were projected by taking into account the most recent trends, as well as the effects of economic conditions and demographic changes. The projected enrollment rates were then used in the Education Forecasting Model (EDMOD), which consists of age-specific rates by sex and by enrollment levels.

Enrollments by age and age groups from the U.S. Census Bureau were adjusted to NCES totals to compute rates for 1972 through 2002. The first stage of EDMOD is an age-specific enrollment model in which these enrollment rates are projected and applied to age-specific population projections from the U.S. Census Bureau. This stage includes all ages for students enrolled in grades K–12 and for students enrolled in colleges and universities. This stage, which is used separately for each sex, consists of 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.

At the postsecondary level, projections of full-time and part-time college enrollments were considered only for ages 16 and over. College enrollment is negligible for earlier ages. Full-time and part-time enrollments are modeled separately, with each model run by sex. Within an enrollment category, where applicable, college 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. Three alternative projections were made using various economic assumptions. table A3 shows enrollment rates for 2002 and middle alternative projected enrollment rates for 2009 and 2014. table A4 shows the equations used to project the enrollments for men by attendance status. table A5 shows the equations used to project enrollment rates for women by attendance.

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, and secondary ungraded and special. Grade progression rate projections were used for grades 2 through 12. Table A6 shows the public school enrollment rates, and table A7 shows the public school grade progression rates for 2002 and projections for 2009 and 2014. The projected rates in tables A6 and A7 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 degree-granting institutions, by age group, sex, attendance status, and level enrolled by student, and by type and control of institution. These projections for 2009 and 2014 are shown in tables A8 and A9, along with actual values for 2002. 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 A8 and A9 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 2009 and 2014 are shown in table A10, along with actual percents for 2002. 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 2002 and projections for 2009 and 2014 are shown in table A11. The projected rates in table A11 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.

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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 2002 and projections for 2009 and 2014 are shown in table A12.

These projected percents were applied to part-time projections of enrollment by level enrolled and by type and control of institution from the third stage of EDMOD. These equivalent of part-time 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 21 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 0.3, 0.5, 1.1, and 2.6 percent, respectively. For the 1 year out prediction, this means that one would expect the projection to be within 0.3 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 out were 0.3, 0.6, 1.1, and 3.7 percent, respectively, while those for projections of public school enrollment in grades 9–12 were 0.4, 0.7, 1.2, and 2.4 percent for the same lead times.

For projections of total enrollment in degree-granting institutions, an analysis of projection errors based on the past 7 editions of Projections of Education Statistics indicates that the MAPEs for lead times of 1, 2, and 5 years were 1.8, 2.6, and 4.0 percent, respectively. For the 1 year out prediction, this means that one would expect the projection to be within 1.8 percent of the actual value, on the average. For more information on MAPEs, 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
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
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 = 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:
math formula
math formula
where:
Math formulas

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Enrollment in Degree-Granting Institutions

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
j = Subscript denoting sex
k = Subscript denoting attendance status
Eijkt = Enrollment of students age i by sex and attendance status
Pijt = Population age i by sex
Rijkt = Enrollment rate for students age i by sex and attendance status
Tijkt = Total enrollment for particular subset of students: full-time men, full-time women, part-time men, part-time women


Then:

math formula

where:
math formula

Methodological Tables

Tables A13 and A14 give the rates used to calculate projections of enrollments and basic assumptions underlying enrollment projections.

Private School Enrollment

This edition is the fourth report that projected trends in elementary and secondary enrollment by grade level in private schools 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, 1999–2000, and 2001–02 were used to develop these projections. In addition, population estimates for 1989 to 2002 and population projections for 2003 to 2014 from the U.S. Census Bureau 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. In contrast, 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 U.S. Census Bureau.

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 secondary ungraded are projected to remain constant at their 2001 levels. To obtain projections of total enrollment, projections of enrollments for the individual grades (kindergarten through 12) and ungraded 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 this projection method has been developed only recently and there is not yet enough historical information to evaluate model performance. As additional data become available, MAPEs can then be calculated.

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State Level

For the 50 states and the District of Columbia, this edition contains projected trends in elementary and secondary enrollment by grade level in public schools from 2003 to the year 2014. This is the 10th 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 1980 to 2002 were used to develop these projections. This survey does not collect enrollment data for private schools.

Population estimates for 1980 to 2002 and population projections for 2003 to 2014 from the U.S. Census Bureau were used to develop the enrollment projections. Both the population estimates and projections used in this year's update have been revised relative to last year's update. First, the population estimates used in this year's Projections of Education Statistics to 2014 incorporate the Census Bureau's state-level intercensal revisions to the population from 1990 to 1999. These intercensal revisions were released by the Census Bureau to ensure consistency in the data between the 1990 Census and the 2000 Census. Second, due to the timing of the release of the new set of the U.S. Census Bureau's state-level population projections, the old set of state-level population projections were adjusted for use in this year's edition. The old set of state-level population projections from the U.S. Census Bureau are consistent with the 2001 population estimates, but do not take into account the new 2002 estimates that were available, nor do they match with the new set of national-level population projections.

The adjustment of the state-level population projections had two steps. First, the projections for the years 2003 to 2014 were adjusted to match with the new 2002 data using the overlap year of data for 2002. The ratio used to adjust each state's projections was constructed by taking the new estimate for 2002 divided by the old 2002 projection from the old set of state-level population projections from the U.S. Census Bureau that match the 2001 estimate. This level adjustment ensured that the projections were consistent with the new 2002 estimates. A second adjustment was then done to ensure that the sum of the adjusted states summed to the new national totals. The final adjusted state-level projections used to develop the state-level projections for this edition of the Projections of Education Statistics to 2014 both line up with the new 2002 state-level estimates and take into account the new national level, but do not take account new patterns in state by state enrollment that may emerge when the complete population forecast is released.

The changes in both the underlying population estimates and projections impact the final state-level enrollment projections in this year's edition of the Projections of Education Statistics. While the impact varies by state, this year's state-level projections are substantially different than the state-level projections released in last year's publication, Projections of Education Statistics to 2013.

Table A13 describes the number of years, projection methods, and smoothing constants used to project enrollments in public schools. Also included in table A13 is the procedure for choosing the different smoothing constants for the time-series models.

All states, with the exception of Washington, DC, were projected using the same single exponential smoothing parameter. Due to the quality of the Washington, DC data, the smoothing parameters for Washington DC were estimated using a feature of the model software EViews 4.1 using the available historical data. This approach yielded more consistent projections of Washington, DC enrollments.

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 U.S. Census Bureau.

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 secondary ungraded are projected to remain constant at their 2002 levels. To obtain projections of total enrollment, projections of enrollments for the individual grades (kindergarten through 12) and ungraded 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.

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