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Projections of Education Statistics to 2019

NCES 2011-017
March 2011

Introduction to Projection Methodology: Expenditures for Public Elementary and Secondary Education


Projections in this edition

This edition of Projections of Education Statistics presents projections of total current expenditures for public elementary and secondary education, current expenditures per pupil in fall enrollment, and current expenditures per pupil in average daily attendance for 2007–08 through 2019–20.

As the source of the elementary and secondary private school data, the NCES Private School Universe Survey, does not collect data for current expenditures, there are no projections for private school current expenditures.

Overview of approach

Theoretical and empirical background

The Public Elementary and Secondary Education Current Expenditure Model used in this report is based on the theoretical and empirical literature on the demand for local public services such as education.2 Specifically, it is based on a type of model that has been called a median voter model. In brief, a median voter model posits that spending for each public good in the community (in this case, spending for education) reflects the preferences of the “median voter” in the community. This individual is identified as the voter in the community with the median income and median property value. The amount of spending in the community reflects the price of education facing the voter with the median income, as well as his income and tastes. There are competing models in which the level of spending reflects the choices of others in the community, such as government officials.

In a median voter model, the demand for education expenditures is typically linked to four different types of independent variables: (1) measures of the income of the median voter; (2) measures of intergovernmental aid for education going indirectly to the median voter; (3) measures of the price to the median voter of providing one more dollar of education expenditures per pupil; and (4) any other variables that may affect one’s tastes for education. The Public Elementary and Secondary Education Current Expenditure Model contains independent variables of the first two types. It uses multiple linear regression analysis to define the relationships between these independent variables and current expenditures (the dependent variable).

Elementary and Secondary Education Current Expenditure Model

Projections for current expenditures per pupil in fall enrollment were produced first. These projections were then used in calculating total expenditures and expenditures per pupil in average daily attendance.

Steps used to project current expenditures for public elementary and secondary education

Step 1. Produce projections of local governments’ education revenue from state sources. The equation for local government’s education revenue included an AR(1) term for correcting for autocorrelation and the following independent variables:

  • disposable income per capita in constant dollars; and
  • the ratio of fall enrollment to the population.

To estimate the model, it was first transformed into a nonlinear model and then the coefficients were estimated simultaneously by applying a Marquardt nonlinear least squares algorithm to the transformed equation.

Step 2. Produce projections of current expenditures per pupil in fall enrollment. The equation for current expenditures per pupil for fall enrollment included an AR(1) term for correcting for autocorrelation and the following independent variables:

  • disposable income per capita in constant dollars; and
  • local governments’ education revenue from state sources per capita in constant dollars. This va-riable was projected in step 1.

To estimate the models, they were first transformed into nonlinear models and then the coefficients were estimated simultaneously by applying a Marquardt nonlinear least squares algorithm to the transformed equation.

For details on the equations used in steps 1 and 2, the data used to estimate these equations, and their results, see “Data and equations used for projections of current expenditures for public elementary and secondary education,” below.

Step 3. Produce projections of total current expenditures. Projections of total current expenditures were made by multiplying the projections for current expenditures per pupil in fall enrollment by projections for fall enrollment.

Step 4. Produce projections of current expenditures per pupil in average daily attendance. The projections for total current expenditures were divided by projections for average daily attendance to produce projections of current expenditures per pupil in average daily attendance.

All the projections were developed in 1982–84 dollars and then placed in 2007–08 dollars using the projections of the Consumer Price Index. Current-dollar projections were produced by multiplying the constant-dollar projections by projections for the Consumer Price Index. The Consumer Price Index and the other economic variables used in calculating the projections presented in this report were placed in school year terms rather than calendar year terms.

Data and equations used for projections of current expenditures for public elementary and secondary education

Data used to estimate the equations for revenue from state sources and current expenditures per pupil. The following data for the period from 1973–74 to 2006–07 were used to estimate the equations:

  • Current expenditures and revenues from state sources—For 1973–74 and 1975–76, the current expenditures data came from Statistics of State School Systems, published by NCES. For 1974–75 and 1976–77, the current expenditures data came from Revenues and Expenditures for Public Elementary and Secondary Education, also published by NCES. For 1977–78 through 2006–07, these data came from the NCES Common Core of Data (CCD) and unpublished data. For most years, the sources for the past values of revenue from state sources were identical to the sources for current expenditures.
  • Disposable personal income per capita—Disposable personal income from the Bureau of Economic Analysis were divided by population data from the U.S. Census Bureau.
  • Fall enrollment to population data—Fall enrollment data from the CCD were divided by population data from the U.S. Census Bureau.

Estimated equations and model statistics for revenue from state sources and current expenditures per pupil. For the results of the equations, see table A-13 on page 116. In each equation, the independent variables affect the dependent variable in the expected way. In the revenues from state sources equation:

  • All other things being equal, as disposable income per capita increases so does local governments’ education revenue from state sources per capita; and
  • As enrollment increases relative to the population, so does the local governments’ education revenue from state sources per capita.
  • In the current expenditures per pupil equation: All other things being equal, as disposable income per capita increases, so does current expenditures per pupil; and
  • As local governments’ education revenue from state sources per capita increases, so does current expenditures per pupil.

Projections for economic variables. Projections for economic variables, including disposable income and the Consumer Price Index, were from the “U.S. Monthly Model: November 2009 Short-Term Projections” from the economic consulting firm, IHS Global Insight (see supplemental table B-6). The values of all the variables from IHS Global Insight were placed in school-year terms. The school-year numbers were calculated by taking the average of the last two quarters of one year and the first two quarters of the next year.

Projections for fall enrollment. The projections for fall enrollment are those presented in section 1 of this publication. The methodology for these projections is presented in Section A.1. Elementary and Secondary Enrollment, earlier in this appendix.

Projections for population. Population estimates for 1973 to 2008 and population projections for 2009 to 2019 from the U.S. Census Bureau were used to develop the public school current expenditure projections. The set of population projections used in this year’s Projections of Education Statistics are the Census Bureau’s 2008 National Population Projections (August 2008).

Historical data for average daily attendance. For 1973–74 and 1975–76, these data came from Statistics of State School Systems, published by NCES. For 1974–75 and 1976–77, the current expenditures data came from Revenues and Expenditures for Public Elementary and Secondary Education, also published by NCES. For 1977–78 through 2006–07, these data came from the CCD and unpublished NCES data.

Projections for average daily attendance. These projections were made by multiplying the projections for enrollment by the average value of the ratios of average daily attendance to enrollment from 1993–94 to 2006–07; this average value was approximately 0.93.

Accuracy of projections

Mean absolute percentage errors (MAPEs) for projections of current expenditures for public elementary and secondary education were calculated using the last 19 editions of Projections of Education Statistics. Exhibit A-6, below, shows the MAPEs for projections of current expenditures.

Exhibit A-6. Mean absolute percentage errors (MAPEs), by lead time for current expenditures for public elementary and secondary education: 2010

Statistic Lead time (years)
1 2 3 4 5 6 7 8 9 10
Total current expenditures 1.2 2.1 2.2 2.3 2.7 3.5 4.2 4.3 4.1 4.4
Current expenditures per pupil in fall enrollment 1.2 2.0 2.0 2.3 3.1 3.7 4.7 4.9 5.6 5.8
NOTE: In constant dollars based on the Consumer Price Index for all urban consumers, Bureau of Labor Statistics, U.S. Department of Labor. MAPEs for current expenditures were calculated using projections from the last 19 editions of Projections of Education Statistics containing current expenditure projections. Calculations were made using unrounded numbers. Some data have been revised from previously published numbers.
SOURCE: U.S. Department of Education, National Center for Education Statistics, Projections of Education Statistics, various issues. (This table was prepared February 2010.)

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

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2 For a discussion of the theory together with a review of some of the older literature, see Inman (1979). More recent empirical work includes Gamkhar and Oates (1996) and Mitias and Turnbull (2001).

 

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Table A-13. Estimated equations and model statistics for current expenditures per pupil in fall enrollment for public elementary and secondary schools, and education revenue from state sources per capita

Dependent variable Equation1 R2 Breusch-Godfrey Serial Correlation LM test statistic2 Time period
Current expenditures
per pupil
ln(CUREXP) =   0.58 + 0.64ln(PCI) + 0.20ln(SGRANT) + 0.92AR(1) 0.996 2.60 (0.27) 1973–74 to
      (0.381)   (3.892)   (2.364)   (17.622)     2006–07
                           
Education revenue
from state sources
per capita
ln(SGRNT) =   0.92 + 1.11ln(PCI) + 0.72ln(ENRPOP) + 0.55AR(1) 0.987 2.02 (0.37) 1973–74 to
      (0.749)   (19.170)   (4.237)   (4.138)     2006–07
                         
1AR(1) indicates that the model included an AR(1) term for correcting for first-order autocorrelation. To estimate the model, it was first transformed into a nonlinear model and then the coefficients were estimated simultaneously by applying a Marquardt nonlinear least squares algorithm to the transformed equation. For a general discussion of the problem of autocorrelation, and the method used to forecast in the presence of autocorrelation, see Judge, G., Hill, W., Griffiths, R., Lutkepohl, H., and Lee, T. The Theory and Practice of Econometrics, New York: John Wiley and Sons, 1985, pp. 315–318.
2Number in parentheses is Prob. Chi-Square(2) associated with the Breusch-Godfrey Serial Correlation LM Test. A p value greater than 0.05 implies that we do not reject the null hypothesis of no autocorrelation at the 5 or 10 percent significance levels. For an explanation of the Breusch-Godfrey Serial Correlation LM test statistic, see Greene, W. (2000). Econometric Analysis. New Jersey: Prentice-Hall.
NOTE: R2 indicates the coefficient of determination. Numbers in parentheses are t-statistics.
CUREXP = Current expenditures of public elementary and secondary schools per pupil in fall enrollment in constant 1982–84 dollars.
SGRANT = Local governments' education revenue from state sources, per capita, in constant 1982–84 dollars.
PCI = Disposable income per capita in constant 2000 chained dollars.
ENRPOP = Ratio of fall enrollment to the population.
SOURCE: U.S. Department of Education, National Center for Education Statistics, Elementary and Secondary School Current Expenditures Model, 1973–74 through 2006–07; and Revenue Receipts from State Sources Model, 1973–74 through 2006–07. (This table was prepared January 2010.)

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