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Projections of Education Statistics to 2020

NCES 2011-026
September 2011

Introduction to Projection Methodology: Elementary and Secondary Enrollment

Projections in this edition

This edition of Projections of Education Statistics presents projected trends in elementary and secondary enrollment from 2009 to 2020. These projections were made using three models:

  • The National Elementary and Secondary Enrollment Model was used to project total, public, and private school enrollments for the nation by grade level and for ungraded elementary and ungraded secondary programs.
  • The State Public Elementary and Secondary Enrollment Model was used to project total public school enrollments by grade level for individual states and regions.
  • The National Public Elementary and Secondary Enrollment by Race/Ethnicity Model was used to project public school enrollments for the nation by race/ethnicity and grade level.

All three elementary and secondary enrollment models used the following same methods.

Overview of approach

Two methods were used in all the elementary and secondary enrollment models:

  • The grade progression rate method was used to project enrollments in grades 2 through 12. In this method, a rate of progression from each grade (1 through 11) to the next grade (2 through 12) was projected using single exponential smoothing. (For example, the rate of progression from grade 2 to grade 3 is the current year's grade 3 enrollment expressed as a percentage of the previous year's grade 2 enrollment.) To calculate enrollment for each year in the forecast period, the progression rate for each grade was applied to the previous year's enrollment in the previous grade.
  • The enrollment rate method was used to project prekindergarten, kindergarten, and first-grade enrollments as well as elementary special and ungraded and secondary special and ungraded enrollments. For each of these enrollment categories, the enrollment rate for the last year of actual data was used as the projected enrollment rate. To calculate enrollment for each year in the forecast period, the enrollment rate for each category was applied to the projected population in the appropriate age group.

Assumptions underlying these methods

The grade progression and enrollment rate methods assume that past trends in factors affecting public and private elementary and secondary school enrollments will continue over the forecast 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 between public and private schools.

For more details on the use of the grade progression and enrollment rate methods, see "Procedures and equations used in all three elementary and secondary enrollment models," below.

Procedures and equations used in all three elementary and secondary enrollment models

The notation and equations that follow describe the basic procedures used to project elementary and secondary enrollments in each of the three elementary and secondary enrollment models.

Let: i = Subscript denoting age
j = Subscript denoting grade
t = Subscript denoting time
T = Subscript of the first year in the forecast period
Nt = Enrollment at the prekindergarten (nursery) level
Kt = Enrollment at the kindergarten level
Gj,t = Enrollment in grade j
Et = Enrollment in elementary special and ungraded programs
St = Enrollment in secondary special and ungraded programs
Pi,t = Population age i
Rj,t = Progression rate for grade j
RNt = Enrollment rate for prekindergarten (nursery school)
RKt = Enrollment rate for kindergarten
RG1,t = Enrollment rate for grade 1
REt = Enrollment rate for elementary special and ungraded programs
RSt = Enrollment rate for secondary special and ungraded programs.

Step 1. Calculate historical grade progression rates for each of grades 2 through 12. The first step in projecting the enrollments for grades 2 through 12 using the grade progression method was to calculate, for each grade, a progression rate for each year in the sample period except for the first year. The progression rate for grade j in year t equals

equation

Step 2. Produce a projected progression rate for each of grades 2 through 12. Projections for each grade's progression rate were then produced for the forecast period using single exponential smoothing. A separate smoothing constant, chosen to minimize the sum of squared forecast errors, was used to calculate the projected progression rate for each grade. Single exponential smoothing produces a single forecast for all years in the forecast period. Therefore, for each grade j, the projected progression rate, symbol, is the same for each year in the forecast period.

Step 3. Calculate enrollment projections for each of grades 2 through 12. For the first year in the forecast period, T, enrollment projections, symbol, for grades 2 through 12, were produced using the projected progression rates and the enrollments of grades 1 through 11 from the last year of actual data, T–1. Specifically,

equation

This same procedure was then used to produce the projections for the following year, T+1, except that enrollment projections for year T were used rather than actual numbers:

equation

The enrollment projections for grades 2 through 11 for year T were those just produced using the grade progression method. The projection for grade 1 for year T was produced using the enrollment rate method, as outlined in steps 4 and 5 below.

The same procedure was used for the remaining years in the projections period.

Step 4. For the last year of actual data, calculate enrollment rates for prekindergarten, kindergarten, grade 1, elementary special and ungraded, and secondary special and ungraded. The first step in projecting prekindergarten, kindergarten, first-grade, elementary special and ungraded, and secondary special and ungraded enrollments using the enrollment rate method was to calculate enrollment rates for each enrollment category for the last year in the sample period, T–1, where:

equation

These enrollment rates were then used as the projected enrollment rates for each year in the sample period (symbol.)

Step 5. Using the rates for the last year of actual data as the projected enrollment rates, calculate enrollment projections for prekindergarten through grade 1 and the ungraded categories. For each year in the forecast period, the enrollment rates were then multiplied by the appropriate population projections from the U.S. Census Bureau (symbol) to calculate enrollment projections for prekindergarten (nursery school) (symbol), kindergarten (symbol), first grade (symbol), elementary ungraded (symbol), and secondary ungraded (symbol)

equation

Step 6. Calculate total elementary and secondary enrollments by summing the projections for each grade and the ungraded categories. To obtain projections of total enrollment, projections of enrollments for the individual grades (prekindergarten through 12), elementary ungraded, and secondary ungraded were summed.

National Elementary and Secondary Enrollment Model

This model was used to project national total, public, and private school enrollments by grade level and for ungraded elementary and ungraded secondary programs. National enrollment projections for public and private schools were developed separately, then added together to yield total elementary and secondary enrollment projections for the nation. To develop these projections, enrollment data from NCES were used, along with population estimates and projections from the U.S. Census Bureau. Below is information about the specific data used to develop the public school projections and the private school projections, as well as information about the grade progression rates and enrollment rates specific to public schools and private schools.

For details on procedures used to develop the projections, see "Procedures and equations used in all three elementary and secondary enrollment models," earlier in this section of appendix A.

Data used to develop national elementary and secondary enrollment projections

Public school enrollment data. Public school enrollment data from the NCES Common Core of Data (CCD) for 1972 to 2008 were used to develop the national public school enrollment projections.

Private school enrollment data. Private school enrollment data from the NCES Private School Universe Survey (PSS) for 1989–90, 1991–92, 1993–94, 1995–96, 1997–98, 1999–2000, 2001–02, 2003–04, 2005–06, 2007–08, and 2009–10 were used to develop the national private school enrollment projections. Since the PSS is collected in the fall of odd numbered years, data for even numbered years without a PSS collection were estimated by interpolating grade-by-grade progression data from PSS.

Population estimates and projections used for public school enrollment projections. Population estimates for 1972 to 2009 and population projections for 2010 to 2020 from the U.S. Census Bureau were also used to develop the public school enrollment projections. The set of population projections used in this year's Projections of Education Statistics are the Census Bureau's 2008 National Population Projections by age and sex (August 2008), adjusted to line up with the most recent historical estimates. This was done through the use of ratio adjustments in which, for each combination of state, age, and sex, the population projections from 2010 to 2020 were multiplied by the ratio of the population estimate for 2009 to the population projection for 2009.

Population estimates and projections used for private school enrollment projections. Population estimates for 1989 to 2009 and population projections for 2010 to 2020 from the U.S. Census Bureau were used to develop the private school enrollment projections. The population projections were ratio-adjusted to line up with the most recent historical estimates.

Grade progression and enrollment rates for national elementary and secondary enrollment projections

Public school grade progression and enrollment rates. Table A-5 on page 91 shows the public school grade progression rates for 2008 and projections for 2009 through 2020. Table A-6 on page 91 shows the public school enrollment rates for 2008 and projections for 2009 through 2020.

Accuracy of national elementary and secondary enrollment projections

Mean absolute percentage errors (MAPEs) for projections of public school enrollment were calculated using the last 27 editions of Projections of Education Statistics, while MAPEs for projections of private school enrollment were calculated using the last nine editions. Table A, below, shows MAPEs for both public and private school enrollment projections.

For more information, see Table A.

For more information about MAPEs, see Section A.0. Introduction, earlier in appendix A.

State Public Elementary and Secondary Enrollment Model

This edition of Projections of Education Statistics contains projected trends in public elementary and secondary enrollment by grade level from 2009 to 2020 for each of the 50 states and the District of Columbia, as well as for each region of the country. The state enrollment projections were produced in two stages:

  • first, an initial set of projections for each state was produced; and
  • second, these initial projections were adjusted to sum to the national public enrollment totals produced by the National Elementary and Secondary Enrollment Model.

For each region, the enrollment projections equaled the sum of enrollment projections for the states within that region.

Initial set of state projections

The same methods used to produce the national enrollment projections—namely, the grade progression rate method and the enrollment rate method—were used to produce the initial sets of public school enrollment projections for each state and the District of Columbia. A separate smoothing constant, chosen to minimize the sum of squared forecast errors, was used to calculate the projected progression rate for each combination of jurisdiction and grade.

For details on the procedures used to develop the initial sets of projections, see "Procedures and equations used in all three elementary and secondary enrollment models," earlier in this section of appendix A.

Limitations of the grade progression method for state projections

The grade progression rate method assumes that past trends in factors affecting public school enrollments will continue over the forecast 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.

Adjustments to the state projections

The initial projections of state public school enrollments were adjusted to sum to the national projections of public school prekindergarten (PK)–12, PK–8, and 9–12 enrollments shown in table 1 on page 31. This was done through the use of ratio adjustments in which all the states' initial 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.

Data used to develop state elementary and secondary enrollment projections

Public school enrollment data. Public school enrollment data from the NCES Common Core of Data (CCD) for 1980 to 2008 were used to develop these projections.

Population estimates and projections. Population estimates for 1980 to 2009 and population projections for 2010 to 2020 from the U.S. Census Bureau were used to develop the state-level enrollment projections. The set of population projections used in this year's Projections of Education Statistics are the Census Bureau's set of interim state-level population projections by age and sex (April 2005). In order for the state-level population projections to be consistent with the most recent historical estimates released by the Census Bureau, these projections were adjusted to line up with the most recent historical estimate for each state. This was done through the use of ratio adjustments in which, for each combination of state, age, and sex, the population projections from 2010 to 2020 were multiplied by the ratio of the population estimate for 2009 to the population projection for 2009.

Accuracy of state elementary and secondary enrollment projections

Mean absolute percentage errors (MAPEs) for projections of public school enrollment by state were calculated using the last 15 editions of Projections of Education Statistics. Tables A-7 through A-9 on pages 92-97 show MAPEs for PK–12, PK–8, and 9–12 enrollment in public elementary and secondary schools by state.

National Public Elementary and Secondary Enrollment by Race/Ethnicity Model

This edition of Projections of Education Statistics contains projected trends in national public elementary and secondary enrollment by race/ethnicity from 2009 to 2020. The enrollment projections by race/ethnicity were produced in two stages:

  • first, an initial set of projections by race/ethnicity was produced; and
  • second, these initial projections were adjusted to sum to the national totals.

Initial set of projections by race/ethnicity

The same methods used to produce the national enrollment projections—namely, the grade progression rate method and the enrollment rate method—were used to produce initial sets of projections for each of the following five racial/ethnic groups: White, Black, Hispanic, Asian/Pacific Islander, and American Indian/Alaska Native. A separate smoothing constant, chosen to minimize the sum of squared forecast errors, was used to calculate the projected progression rate for each combination of race/ethnicity and grade.

For details on the procedures used to develop the initial sets of projections, see "Procedures and equations used in all three elementary and secondary enrollment models," earlier in this section of appendix A.

Adjustments to the projections by race/ethnicity

The initial projections of enrollments by race/ethnicity were adjusted to sum to the national projections of public school PK–12, PK–8, and 9–12 enrollments shown in table 1 on page 31. This was done through the use of ratio adjustments in which all the initial enrollment projections by race/ethnicity for each grade level were multiplied by the ratio of the national enrollment projection for that grade level to the sum of the initial enrollment projections by race/ethnicity for that grade level.

Data and imputations used to develop enrollment projections by race/ethnicity

Public school enrollment data. Public school enrollment data by grade level and race/ethnicity from the NCES Common Core of Data (CCD) for 1994 to 2008 were used to develop these projections. While projections by race/ethnicity were produced at the national level only, the national data used to develop these projections were constructed from state-level data on enrollment by grade level and race/ethnicity. In those instances where states did not report their enrollment data by grade level and race/ethnicity, the state-level data had to be examined and some imputations made in order to produce the national public school enrollment by grade level and race/ethnicity data. For example, in 1994, North Dakota did not report grade-level enrollment data by race/ethnicity. It did, however, report these numbers for 1995. So, to impute these numbers for 1994, North Dakota's 1994 grade-level enrollment data were multiplied by the state's 1995 racial/ethnic breakdowns at each grade level. In 2008, jurisdictions could classify students by an additional racial/ethnic group - those of two or more races. As only five states used this reporting category, those numbers were proportioned among the other five racial/ethnic groups by each of the five ethnic groups' shares of total enrollment, excluding enrollment of those of two or more races. When a sufficient number of states use this racial/ethnic group, projections will be developed for this group.

Population estimates and projections. Population estimates for 2000 to 2009 and population projections for 2010 to 2020 from the U.S. Census Bureau were used to develop the enrollment projections by race/ethnicity. The set of population projections used in this year's Projections of Education Statistics are the Census Bureau's 2008 National Population Projections by age, sex, and race/ethnicity (August 2008), ratio-adjusted to line up with the most recent historical estimates.

Accuracy of enrollment projections by race/ethnicity

Because this is the second edition of Projections of Education Statistics to include projections of elementary and secondary public school enrollments by race/ethnicity, the difference between the projections and actual data for the same years cannot yet be determined.

For more information, see Table A-5 through table A-9.

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