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William J. HussarEnrollment 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 2017. 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 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 2005 and projections for 2006 through 2017. 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.
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 2017 are shown in tables A-8 and A-9, along with actual values for 2006. 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 2017 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 2006 and projections for 2007 through 2017 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.
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 2006 and projections for 2007 and 2017 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.
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 2006. 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. Table A-14 shows the estimated equations used to project the enrollments for White men by attendance status. Table A-15 shows the estimated equations used to project enrollment rates for White women by attendance. Table A-16 shows the estimated equations used to project the enrollments for Black men by attendance status. Table A-17 shows the estimated equations used to project enrollment rates for Black women by attendance. Table A-18 shows the estimated equations used to project the enrollments for Hispanic men by attendance status. Table A-19 shows the estimated equations used to project enrollment rates for Hispanic women by attendance. Table A-20 shows the estimated equations used to project the enrollments for Asian or Hawaiian-Pacific Islander men by attendance status. Table A-21 shows the estimated equations used to project enrollment rates for Asian or Hawaiian-Pacific Islander women by attendance status.
An analysis of projection errors from the past 24 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.
The notation and equations that follow describe the basic models used to project 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:
where:
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 25–29t = Subscript denoting year
i = 26: ages 30–34
i = 27: ages 35 and over for enrollment (35–44 for population)
Then:
where:
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 25–29t = Subscript denoting year
i = 26: ages 30–34
i = 27: ages 35 and over for enrollment (35–44 for population)
Then:
where:
Table A-22 gives the basic assumptions underlying enrollment projections.
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 NCES Private School Universe Survey for 1989–90, 1991–92, 1993–94, 1995–96, 1997–98, 1999–2000, 2001–02, 2003–04, and 2005–06 were used to develop these projections. In addition, population estimates for 1989 to 2006 and population projections for 2007 to 2017 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-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. 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 2005 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 model performance. As additional data become available, MAPEs can then be calculated.
This edition contains projected trends in public elementary and secondary enrollment by grade level from 2006 to the year 2017 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 2005 were used to develop these projections. This survey does not collect enrollment data for private schools.
Population estimates for 1980 to 2006 and population projections for 2007 to 2017 from the U.S. Census Bureau were used to develop the enrollment projections. The set of population projections used in this year's Projections of Education Statistics to 2017 are the Census Bureau's set of interim state-level population projections (April 2005), which were also used in last year's report. This set of state-level projections line up with the Census Bureau's 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 A13 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 2005 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.
The projections of state enrollments were adjusted to sum to the national projections of public school K–12, K–8, and 9–12 enrollments shown in table 1. This was done through the use of ratio adjustments in which all the states' enrollment projections for each grade level were multiplied by the ratio of the national enrollment projection for that grade level to the sum of the state enrollment projections for that grade level. For details on the methods used to develop the national projections for this statistic, see the section on national enrollment projections in this appendix.
For each region, the enrollment projections equaled the sum of enrollment projections within its region.
