The elementary and secondary education current expenditure model is based on the theoretical and empirical literature on the demand for local public services such as education.2
The model that is the basis for the elementary and secondary education current expenditure model has been called the median voter model. In brief, the theory states 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 the "bureaucrats."
In a median voter model, the demand for education expenditures is typically linked to four different types of 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 elementary and secondary school current expenditure model contains variables reflecting the first two types of variables. The model is:
ln(CUREXPt) = b0 + b1ln(PCIt) + b2ln(SGRNTt)
ln indicates the natural log;
CUREXPt equals current expenditures of public elementary and secondary schools per pupil in fall enrollment in constant 1982–84 dollars in year t;
PCIt equals disposable income per capita in constant 2000 dollars in year t; and
SGRNTt equals local governments' education revenue from state sources, per capita, in constant year 1982–84 dollars in year t. The model used to project this variable is discussed below.
The model was estimated using least squares with the AR(1) process for correcting for autocorrelation. The model was estimated using data from 1973–74 to 2005–06.
There are potential problems with using a model for local government education expenditures for the nation as a whole. Two such problems concern the variable SGRNT. First, the amount of money that local governments receive for education from state governments varies substantially by state. Second, the formulas used to apportion state moneys for education among local governments vary by state.
Beginning in 1988–89, there was a major change in the survey form used to collect data on current expenditures (the National Public Education Financial Survey). This new survey form produces a more complete measure of current expenditures; therefore, the values for current expenditures are not completely comparable to the previously collected numbers. Data for a majority of states were also collected for 1986–87 and 1987–88 that were comparable to data from the new survey form. A comparison of these data with those from the old survey form suggests that the use of the new survey form may have increased the national figure for current expenditures by approximately 1.4 percent over what it would have been if the survey form had not been changed. When the model was estimated, all values for current expenditures before 1988–89 were increased by 1.4 percent.
The results for the model are shown in table A-27. Each variable affects current expenditures in the direction that would be expected. With high levels of income (PCI) or revenue from state sources (SGRNT), the level of spending increases.
From the cross-sectional studies of the demand for education expenditures, we have an estimate of how sensitive current expenditures are to changes in PCI. We can compare the results from this model with those from the cross-sectional studies. For this model, an increase in PCI of 1 percent, with SGRNT held constant, would result in an increase of current expenditures per pupil in fall enrollment of approximately .6 percent. With PCI held constant, an increase of 1 percent in SGRNT would result in an increase in current expenditures per pupil in fall enrollment of approximately .2 percent. Both numbers are well within the range of what has been found in cross-sectional studies.
The results from this model are not completely comparable with those in editions prior to the Projections of Education Statistics to 2014. First, in those earlier editions, the sample period used to estimate the model began with either 1959–60 or 1967–68 rather than 1969–70. This change was made due to superior model diagnostics. Second, in some earlier editions the model contained an additional variable, as a proxy for the price facing the median voter, the ratio of enrollment to the population. This price variable has been excluded due to its lack of statistical significance as measured by its t-statistic. Third, in editions prior to Projections of Education Statistics to 2011 and Projections of Education Statistics to 2013, 2 average daily attendance rather than fall enrollment, was used as the measure of enrollment. This change was made because the definitions of fall enrollment are more consistent from state to state than those of average daily attendance.
There have been other changes to the model used in earlier editions. As with the current expenditure projections in the most recent editions, the population number for each school year is the U.S. Census Bureau's July 1 population number for the upcoming school year. In earlier editions, the school year population numbers were from an economic consulting firm. These changes were made to be consistent with population projections used in producing other projections of education statistics. Also, there have been changes in the definition of disposable income.
Projections for total current expenditures were made by multiplying the projections for current expenditures per pupil in fall enrollment by projections for fall enrollment.
The projections for total current expenditures were also divided by projections for average daily attendance to produce projections of current expenditures per pupil in average daily attendance to provide projections that are consistent with those from earlier years. Projections were developed in 1982–84 dollars and then placed in 2006–07 dollars using 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.
Three alternative sets of projections for current expenditures are presented: the middle alternative projections, the low alternative projections, and the high alternative projections. The alternative sets of projections differ because of varying assumptions about the growth paths for disposable income and revenue from state sources. The alternative sets of projections for the economic variables, including disposable income, were from the "U.S. Quarterly Model: November 2008: Long-Term-Projections" of the economic consulting firm IHS Global Insight of the economic consulting firm Global Insight, Inc. (supplemental table B-6).
IHS Global Insight’s November 2008 trend scenario was used as a base for the middle alternative projections of the economic variables. IHS Global Insight’s trend scenario depicts a mean of possible paths that the economy could take over the forecast period, barring major shocks. The economy, in this scenario, evolves smoothly, without major fluctuations.
IHS Global Insight’s November 2008 pessimistic scenario was used for the low alternative projections, and IHS Global Insight’s November 2008 optimistic scenario was used for the high alternative projections.
In the middle alternative projections, disposable income per capita rises each year from 2006–07 to 2017–18 at rates between 0.4 percent and 2.7 percent. In the low alternative projections, disposable income per capita ranges between 0.4 percent and 2.3 percent, and in the high alternative projections, disposable income per capita rises at rates between 0.4 percent and 3.6 percent.
The alternative projections for revenue from state sources, which form a component of the current expenditures model, were produced using the following model:
ln(SGRNTt) = b0 + b1ln(PCIt) + b2ln(ENRPOPt)
ln indicates the natural log;
SGRNTt equals local governments' education revenue from state sources, per capita, in constant 1982–84 dollars in year t;
ENRPOPt equals the ratio of fall enrollment to the population in year t; and
PCIt equals disposable income per capita in constant 2000 dollars in year t.
The model was estimated using least squares with the AR(1) process for correcting for autocorrelation. The model was estimated using the period from 1971–72 to 2004–05. These models are shown in table A-29.
The values of the coefficients in this model follow expectations. As the enrollment increases relative to the population (higher ENRPOP), so does the amount of aid going to education. Finally, other things being equal, as the value of disposable income per capita in real dollar values (higher PCI) increases, the level of local governments' education revenue from state sources per capita also increases.
This year's edition of the Projections of Education Statistics uses the same revenue from state sources model as the last three year's editions. The model used in the prior two editions, Projections of Education Statistics 2012 and Projections of Education Statistics 2013, was different. It included a term for personal taxes and non-tax receipts (PERTAX1) and an inflation rate term (RCPIANN) and was estimated over a different time period (the sample period began in 1967–68 rather than 1971–72). The current model specification yielded superior model diagnostics than the model used in the Projections of Education Statistics 2012 and Projections of Education Statistics 2013. The models in the five most recent editions of the Projections of Education Statistics each used the same variable to represent enrollment (ENRPOP). In the earlier editions, models used average daily attendance rather than fall enrollment as the measure of enrollment, and the sample period used to produce the forecast began in 1959–60. As with the current expenditures model, the change to fall enrollment was done because the definition of fall enrollment is more consistent across states, and the change in sample period was done because of superior model diagnostics. Other models in the past have contained a second measure of state and local government revenue. Also in earlier editions, similar models were used except the variables were not in log form. Both of these changes were made because of superior model diagnostics.
Three alternative sets of projections for SGRNT were produced using this model. Each is based on a different set of projections for revenue from state sources per capita. The middle set of projections was produced using the values from the middle set of alternative projections. The low set of projections was produced using the values from the low set of alternative projections, and the high set of projections was produced using the values from the high set of alternative projections. In the middle alternative projections, revenue from state sources per capita changes each year from 2007–08 to 2018–19 at rates between 0.05 percent and 3.6 percent. In the low alternative projections, revenue from state sources per capita ranges between -1.7 percent and 3.6 percent, and in the high alternative projections, revenue from state sources per capita changes at rates between -1.1 percent and 3.9 percent.
Eighteen of the last 19 editions of Projections of Education Statistics contained projections of current expenditures. The actual values of current expenditures can be compared with the projected values in the previous editions to examine the accuracy of the model.
In most of the earlier editions of Projections of Education Statistics, average daily attendance rather than fall enrollment was used as the measure of enrollment in the calculation of the current expenditure per pupil projection. However, projections of current expenditures per fall enrollment were presented in most of these earlier editions, and projections of fall enrollment were presented in all of these earlier editions. As a result, the projected values of both current expenditures per pupil in fall enrollment and current expenditures per pupil in average daily attendance can be compared to their respective actual values.
Similar sets of independent variables have been used in the production of the current expenditure projections presented in the last 16 editions of Projections of Education Statistics, including this one. The one major change is that in all the earlier editions except the two previous editions of the Projections of Education Statistics, the set of variables included the ratio of the number of students to the population.
Several commonly used statistics can be used to evaluate projections. The values for one of these, the mean absolute percentage error (MAPE), are presented in table A-2. MAPEs of expenditure projections are presented for total current expenditures, current expenditures per pupil in fall enrollment, current expenditures per pupil in average daily attendance, and teacher salaries.
An analysis of projection errors from similar models used in the past seventeen editions of Projections of Education Statistics that contained expenditure projections indicates that mean absolute percentage errors (MAPEs) for total current expenditures in constant dollars were 1.3 percent for 1 year out, 2.1 percent for 2 years out, 2.8 percent for 5 years out, and 4.5 percent for 10 years out. For the 1-year-out prediction, this means that one would expect the projection to be within 1.3 percent of the actual value, on average. MAPEs for current expenditure per pupil in fall enrollment in constant dollars were 1.3 percent for 1 year out, 2.0 percent for 2 years out, 3.1 percent for 5 years out, and 5.8 percent for 10 years out. For more information on the MAPEs, see table A-2.
Data from several different sources were used to produce the projections in this report. In some instances, the time series used were made by either combining numbers from various sources or manipulating the available numbers. The sources and the methods of manipulation are described here.
The time series used for current expenditures was compiled from several different sources. For the school years ending in even numbers from 1969–70 to 1975–76, the numbers for current expenditures were taken from various issues of Statistics of State School Systems, published by NCES. For the school years ending in odd numbers during the 1970s, up to and including 1976–77, the numbers were taken from various issues of Revenues and Expenditures for Public Elementary and Secondary Education, published by NCES. For the school years from 1977–78 until 2005–06, the data were from the NCES Common Core of Data survey and unpublished data.
For 1974–75 and 1976–77, expenditures for summer schools were subtracted from the published figures for current expenditures. The value for 1972–73 was the sum of current expenditures at the local level, expenditures for administration by state boards of education and state departments of education, and expenditures for administration by intermediate administrative units.
Note that although the data from the different sources are similar, they are not entirely consistent. Also, the NCES data beginning with 1980–81 are not entirely consistent with the earlier NCES numbers, due to differing treatments of items such as expenditures for administration by state governments and expenditures for community services.
An alternative source for current expenditures would have been the U.S. Census Bureau's F-33, which offers statistics at the district level. This level of geographic detail was not needed, however.
For most years, the sources for the past values of average daily attendance were identical to the sources for current expenditures.
Projections for average daily attendance for the period from 2006–07 to 2018–19 were made by multiplying the projections for enrollment by the average value of the ratios of average daily attendance to the enrollment from 1992–93 to 2005–06; this average value was approximately .93.
The values for fall enrollment from 1979–80 to 2006–07 were taken from the NCES Common Core of Data survey. The projections for fall enrollment are those presented in chapter 1 of this publication.
For 1969–70 to 2005–06, the sources for revenue from state sources were the two NCES publications Statistics of State School Systems and Revenues and Expenditures for Public Elementary and Secondary Education, and the NCES Common Core of Data survey. The methods for producing the alternative projections for revenue from state sources are outlined above.
The projected values for disposable income, personal taxes and non-tax receipts to state and local governments, and indirect business taxes and tax accruals to state and local governments were developed using projections developed by Global Insight's U.S. Quarterly Model. Projected values of the Consumer Price Index for all urban consumers, which was used for adjusting current expenditures, revenue from state sources, and the state revenue variables, were also developed using the U.S. Quarterly Model.
The U.S. Census Bureau supplied both the historical and projected values for the population.
The values of all the variables from 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.
The Elementary and Secondary School Price Index was considered as a replacement for the Consumer Price Index for placing current expenditures and teacher salaries in constant dollars. This index could not be used because the required projections of the index were not available. There are other price indexes, such as the implicit price deflator for state and local government purchases, which could have been used instead of the Consumer Price Index. These alternatives would have produced somewhat different projections.