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Projections of Education Statistics to 2018

NCES 2009-062
September 2009

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.

Enrollment data for degree-granting institutions presented in this report are derived from both NCES aggregate enrollment counts and the U.S. Census Bureau age-specific enrollment counts. Specifically, the most detailed level of enrollment data (by age, sex, enrollment status, control of institution, type of institution, and level enrolled) were iteratively changed using proportions that are based on known more aggregate totals to ensure that the sum across these most detailed level of enrollment data equal the more aggregate NCES totals that do not include age.

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 A-3 shows enrollment rates for 2006 and middle alternative projected enrollment rates for 2012 and 2018. Table A-4 shows the estimated equations used to project the enrollments for men by attendance status. Table A-5 shows the estimated equations used to project enrollment rates for women by attendance status. The particular equations shown were selected on the basis of their statistical properties, such as coefficients of determination (R2s), the t-statistics of the coefficients, the Durbin-Watson statistic, the Breusch-Godfrey Serial Correlation LM test statistic, and residual plots.

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

The second stage of EDMOD projects enrollment in public elementary and secondary schools by grade group and by organizational level. Public enrollments by age were based on enrollment rate projections for grade classifications of 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 A-6 shows the public school enrollment rates, and table A-7 shows the public school grade progression rates for 2006 and projections for 2008 through 2018. The projected rates in tables A-6 and A-7 were used to compute the projections of enrollments in elementary and secondary schools, by grade, shown in table 3.

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 2007 through 2018 are shown in tables A-8 and A-9, along with actual values for 2007. 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 A-8 and A-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 2007 through 2018 are shown in table A-10, along with actual percents for 2006. 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 2007 and projections for 2008 through 2018 are shown in table A-11. The projected rates in table A-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.

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. The full-time-equivalent enrollment measures enrollment as if students were enrolled full time for one academic year, and equals the sum of full-time enrollment and full-time-equivalent of part-time enrollment. The full-time-equivalent of part-time enrollment was estimated as a percentage of part-time enrollment. In EDMOD, the full-time-equivalent of part-time enrollment was calculated using different percentages for enrollment category by level enrolled and by type and control of institution. Actual percents for 2007 and projections for 2008 and 2018 are shown in table A-12.

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.

College Enrollment, by Sex, Attendance Status, Age Group, and Race/Ethnicity

The fifth stage of EDMOD projects enrollments in degree-granting institutions by age, sex, attendance status, and race/ethnicity. The race/ethnicity groups projected include the following: White; Black; Hispanic; Asian or Hawaiian-Pacific Islander; American Indian/Alaska Native and Non-Resident Alien. Enrollment projections are based on projected enrollment rates by age, sex, attendance status, and race/ethnicity 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. With the exception of American Indian/Alaska Native and Non-Resident Alien, all race/ ethnicity groups were projected by taking into account the most recent trends, as well as the effects of economic conditions and demographic changes. Due to the nature of the historical data, American Indian/Alaska Native enrollments were projected using single exponential smoothing and Non-Resident Alien enrollments were projected using patterns in recent historical growth.

Enrollments by sex, race/ethnicity and age from the U.S. Census Bureau were adjusted to NCES totals by sex and race/ethnicity to compute rates for 1981 through 2007. As with the first stage of EDMOD, the fifth stage consists of age-specific enrollment models for each sex-race/ethnicity group in which enrollment rates are projected and applied to age-specific population projections by sex and race/ethnicity from the U.S. Census Bureau. The final set of projected rates by age, sex, attendance status, and race/ethnicity were controlled to the stage one enrollment rates by age, sex, and attendance status to ensure consistency across stages. Specifically, the most detailed level of enrollment data (by age, sex, enrollment status, and race/ethnicity) were iteratively changed using proportions that are based on known more aggregate totals to ensure that the sum across these most detailed level of enrollment data equal the more aggregate NCES totals that do not include age.

Stage five consists of 16 individual pooled time series models—one for each attendance status - sex - race/ethnicity combination—that are each pooled across age. As with the stage one postsecondary level projections, projections of full-time and part-time college enrollments by race/ ethnicity were considered only for ages 16 and over. College enrollment is negligible for earlier ages. Within each model, 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. Tables A-14 through A-21 show the estimated equations used to project the enrollments for each racial/ethnic and sex category.

Accuracy of Projections

An analysis of projection errors from the past 25 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, 0.6, 1.3, and 2.3 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 0.4, 0.6, 1.3, and 3.2 percent, respectively, while those for projections of public school enrollment in grades 9–12 were 0.4, 0.7, 1.4, and 2.3 percent for the same lead times.

For projections of total enrollment in degree-granting institutions, an analysis of projection errors based on the past 10 editions of Projections of Education Statistics indicates that the MAPEs for lead times of 1, 2, 5, and 10 years were 1.5, 2.1, 4.6, and 10.9 percent, respectively. For the 1-year-out prediction, this means that one would expect the projection to be within 1.5 percent of the actual value, on the average. For more information on MAPEs, see table A-2.

Basic Methodology

The notation and equations that follow describe the basic models used to project public elementary and secondary enrollment (the grade progression method).1

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
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:

equation
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where:

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Enrollment in Degree-Granting Institutions

For degree-granting institutions, 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:

equation

where:

equation

Enrollment in Degree-Granting Institutions by Race/Ethnicity

Projections for degree-granting institutions by sex and attendance status of student were further disaggregated by race/ethnicity. 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
l = Subscript denoting race/ethnicity
E ijklt= Enrollment of students age i by sex, attendance status, and race/ethnicity
Pijlt = Population age i by sex and race/ethnicity
R ijklt = Enrollment rate for students age i by sex, attendance status, and race/ethnicity
T ijklt = Total enrollment for a particular subset of students by race/ethnicity: full-time men, full-time women, part-time men, part-time women

Then:

equation

where:

equation

First-time Freshmen Enrollment in Degree-Granting Institutions

Projections of first-time freshman enrollment in degree-granting institutions were derived in the following manner. From 1975 to 2007, the ratio of first-time freshman enrollment to undergraduate enrollment was calculated for males and females. These ratios were projected using single exponential smoothing with a smoothing constant of a = 0.4, yielding a constant value over the projection period. This constant value was then applied to projections of undergraduate enrollment by sex to yield projections of first-time freshman enrollment. This method assumes that the future pattern in the trend of first-time freshman enrollment will be the same as that for undergraduate enrollment.

Private School Enrollment

This edition is the seventh 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 biennial NCES Private School Universe Survey (PSS), which is collected in the fall of odd numbered years, were used to develop these projections. Private school enrollment data for alternate years without a PSS collection were estimated using data from the PSS. In addition, population estimates for 1989 to 2007 and population projections for 2008 to 2018 from the U.S. Census Bureau were used to develop the projections.

Prekindergarten, kindergarten, and first-grade enrollments are based on projected enrollment rates of 5- and 6-yearolds. 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. 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. 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 2006 levels. To obtain projections of total enrollment, projections of enrollments for the individual grades (prekindergarten 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 long-term model performance. As additional data become available, MAPEs can then be calculated.

State Level

This edition contains projected trends in public elementary and secondary enrollment by grade level from 2007 to the year 2018 for each of the 50 states and the District of Columbia.

Public school enrollment data from the NCES Common Core of Data survey for 1980 to 2006 were used to develop these projections. This survey does not collect enrollment data for private schools.

Population estimates for 1980 to 2007 and population projections for 2008 to 2018 from the U.S. Census Bureau were used to develop the enrollment projections. The set of population projections used in this yearís Projections of Education Statistics to 2018 are the Census Bureauís set of interim state–level population projections (April 2005). This set of state–level projections corresponds to the Census Bureauís interim national population projections, which were released earlier in May 2004.

Table A–13 describes the number of years, projection methods, and smoothing constants used to project enrollments in public schools. Also included in table A–13 is the procedure for choosing the different smoothing constants for the time–series models. All jurisdictions were projected using the same single exponential smoothing parameter.

As with the national enrollment projections, projections of enrollment in public elementary and secondary schools by state primarily used the grade progression rate method. As with the national projections, prekindergarten, 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 2006 levels. To obtain projections of total enrollment, projections of enrollments for the individual grades (prekindergarten 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 unanticipated 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.


1In the previous three editions of this report, there was an inconsistency with the methodological description and the actual methodology used to produce the projections of enrollment at the nursery and kindergarten levels. Historically, the nursery enrollment counts had been underreported by states. Due to this problem, a single parameter was used for the enrollment rate at the nursery and kindergarten levels. Some years ago there was an improvement in the source data. Hence, beginning with the Projections of Education Statistics to 2015, there was a change in the methodology from a single parameter to two parameters (nursery and kindergarten separate); however, the methodology section had not reflected this change. No changes have been detected in the projections due to this change in methodology.

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