A5. Expenditures of Public Elementary
and Secondary Schools

Econometric techniques were used to produce the projections for current expenditures and average teacher salaries. The equations in this chapter should be viewed as forecasting equations rather than structural equations. The particular equations shown were selected on the basis of their statistical properties, such as coefficients of determination (R²s), the t-statistics of the variables, the Durbin-Watson statistic, and residual plots. These econometric models will yield good forecasting results only if the relationships that existed among the variables in the past continue throughout the projection period.

Elementary and Secondary School Current Expenditure Model

There has been a large body of work, both theoretical and empirical, on the demand for local public services such as education.* The elementary and secondary school current expenditure model is based on this work.

The model that is the basis for the elementary and secondary school 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, 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. Hence, 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." The median voter model was chosen as the basis of the elementary and secondary school current expenditure model as it has been the one most thoroughly studied.

There have been many empirical studies of the demand for education expenditures using the median voter model. In most instances, researchers have used cross-sectional data. The elementary and secondary school current expenditure model was built on the knowledge gained from these cross-sectional studies and was adapted from them for use in a time-series study.

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 three types of variables. The model is:

ln(CUREXP) = b₀ + b₁ln(PCI) + b₂ln(SGRNT)
                      + b₃ln(ENRPOP)

where:

ln indicates the natural log;

CUREXP equals current expenditures of public elementary and secondary schools per pupil in fall enrollment in constant 1982-84 dollars;

PCI equals disposable income per capita in constant 1996 dollars;

SGRNT equals local governments' education revenue receipts from state sources, per capita, in constant year 1982-84 dollars; and

ENRPOP equals the ratio of fall enrollment to the population.

The model was estimated using the AR1 model for correcting for autocorrelation. This was done because the test statistics were significantly better than those from the ordinary least squares (OLS) estimation, and the Durbin-Watson statistic was in the inconclusive region when the model was estimated using OLS. This is the eighth edition of Projections of Education Statistics in which this method of estimation, rather than OLS, was used. Ordinary least squares was used in the previous four editions of Projections of Education Statistics. The model was estimated using the period from 1967-68 to 1998-99.

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 which 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. 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. In a crosswalk study, 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 A5.1. Each variable affects current expenditures in the direction that would be expected. With high levels of income (PCI) or revenue receipts from state source (SGRNT), the level of spending increases. As the number of pupils increases relative to the population (that is, as ENRPOP increases), the level of spending per pupil falls.

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 and ENRPOP. 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 and ENRPOP held constant, would result in an increase of current expenditures per pupil in fall enrollment of approximately 0.67 percent. With PCI and SGRNT held constant, an increase of 1 percent in ENRPOP would result in a decrease in current expenditures per pupil in fall enrollment of approximately 0.33 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 from any of the previous editions of Projections of Education Statistics. First, in earlier editions, average daily attendance, rather than fall enrollment, was used as the measure of enrollment in current expenditure per pupil and the ratio of enrollment to population variables. Second, with this edition the sample period used to estimate the model began with 1967-68 rather than 1959-60 as with previous editions.

There have been other changes with the model used in earlier editions. As with the previous two editions, the population number for each school year is the Bureau of the Census's July 1 population number for the upcoming school year. In earlier editions, each school year's population number was the average of an economic consulting firm's estimated population numbers of each quarter in that school year. Also, there have been changes in the definition of the 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 divided by projections for average daily attendance to produce projections of current expenditures per pupil in average daily attendance. Projections were developed in 1982-84 dollars and then placed in 1999-2000 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 receipts from state sources.

The alternative sets of projections for the economic variables, including disposable income, were developed using three economic scenarios prepared by the economic consulting firm DRI-WEFA.

DRIWEFA's February 2001 trend scenario was used as a base for the middle alternative projections of the economic variables. DRIWEFA'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.

DRIWEFA's February 2001 pessimistic scenario was used for the low alternative projections and DRIWEFA's February 2001 optimistic scenario was used for the high alternative projections.

In the middle alternative projections, disposable income per capita rises each year from 2001-02 to 2010-11 at rates between 2.2 percent and 3.8 percent. In the low alternative projections, disposable income per capita ranges between 1.7 percent and 2.9 percent, and in the high alternative projections, disposable income per capita rises at rates between 2.6 percent and 5.2 percent.

The alternative projections for revenue receipts from state sources were produced using the following model:

ln(SGRNT) = b₀ + b₁ln(PERTAX1)
                   + b₂ln(ENRPOP)
                   + b₃ln(RCPIANN/RCPIANN1)

where:

ln indicates the natural log; SGRNT equals local governments' education revenue receipts from state sources, per capita, in constant 1982-84 dollars;

PERTAX1 equals personal taxes and nontax receipts to state and local governments, per capita, in constant 1982-84 dollars lagged one period;

ENRPOP equals the ratio of fall enrollment to the population;

RCPIANN equals the inflation rate measured by the Consumer Price Index; and

RCPIANN1 equals the inflation rate measured by the Consumer Price Index lagged 1 period.

This equation was estimated using the AR1 model for correcting for autocorrelation. The model was estimated using the period from 1967-68 to 1998-99. These models are shown in table A5.1.

The values of the coefficients in this model follow expectations. As state governments receive more revenue (higher PERTAX1), they have more money to send to local governments for education. As the enrollment increases relative to the population (higher ENRPOP), so does the amount of aid going to education. Finally, the real dollar values of revenue receipts from state governments to local governments would fall, other things being equal, in years with rapidly increasing inflation (higher RCPIANN/RCPIANN1).

The model used in the previous four edition of the Projections of Education Statistics was identical to that used in this edition except that average daily attendance rather than fall enrollment had been used in the ratio of enrollment to population variable and sample period used began in 1959-60. The model used in Projections of Education Statistics to 2006 was identical to the model used in the last four editions except that it contained a second measure of state and local government revenue. In earlier editions, similar models were used except the variables were not in log form.

Three alternative sets of projections for SGRNT were produced using this model. Each is based on a different set of projections for personal taxes and the rate of change in the inflation rate. 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 set of projections, personal taxes and nontax receipts increase at rates between -2.6 percent and 4.2 percent. In the low set of projections, personal taxes and nontax receipts increase at rates between -3.6 percent and 5.8 percent. In the high set of projections, personal taxes and nontax receipts increase at rates between -1.1 percent and 5.6 percent.

In the middle set of projections, revenue receipts from state sources increase at rates between -2.8 percent and 2.3 percent for the period from 2001-02 to 2010-11. In the low set of projections, they increase at rates between -3.4 percent and 2.9 percent. In the high set of projections, they increase at rates between -2.4 percent and 2.8 percent.

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Elementary and Secondary Teacher Salary Model

Most studies conducted on teacher salaries, like those on current expenditures, have used cross-sectional data. Unlike current expenditures models, however, the models for teacher salaries from these existing cross-sectional studies cannot easily be reformulated for use with time-series data. One problem is that we do not have sufficient information concerning the supply of qualified teachers who are not presently teaching. Instead, the elementary and secondary salary model contains terms that measure the demand for teachers in the economy.

The elementary and secondary teacher salary model is:

ln(SALRY) = b₀ + b₁ln(CUREXP) + b₂ln(ENRPOP)
                  + b₃ln(ENR1/ENR2)

where:

ln indicates the natural log; SALRY equals the estimated average annual salary of teachers in public elementary and secondary schools in constant 1982-84 dollars;

CUREXP equals current expenditures of public elementary and secondary schools per pupil in fall enrollment in constant 1982-84 dollars;

ENRPOP equals the ratio of average daily attendance to the population;

ENR1 equals the average daily attendance lagged 1 period; and

ENR2 equals the average daily attendance lagged 2 periods.

The model was estimated using the period from 1969-70 to 1998-99. The AR1 model for correcting for autocorrelation was used as the Durbin-Watson statistic was in the inconclusive region when the model was estimated using OLS.

Due to the effects on current expenditures caused by the change in survey forms discussed above, the values for current expenditures for 1959-60 to 1987-88 were increased by 1.4 percent when the salary model was estimated. The coefficients of the salary model are different than if the unadjusted numbers for current expenditures had been used and hence the forecasts are different.

The results for this model are also shown in table A5.1. There is no literature for comparing the sizes of the coefficients. However, the direction of the impact each variable has on salaries is as expected: as the level of spending per pupil increases (higher CUREXP), more teachers can be hired, so demand for teachers increases and salaries may increase; as the number of students increases (higher ENRPOP and ENR1/ENR2), demand for teachers may increase, so salaries may increase.

The model used in the previous five editions of the Projections of Education Statistics was identical to that used in this edition except that 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 rather than 1969-70. In the seven earlier editions, similar models were used except the variables were not in log form.

As with current expenditures, three different scenarios are presented for teacher salaries. The same projections for ENRPOP and ENR are used for each alternative projection; the sole difference between the projections is in the projection for current expenditures. The middle alternative projection for salaries uses the middle alternative projection for current expenditures. The low alternative projection for salaries uses the low alternative projection for current expenditures. The high alternative projection for salaries uses the high alternative projection for current expenditures.

Current expenditures, average teacher salaries, and the number of teachers are interrelated; analysis was conducted to see whether the projections of these three time series were consistent.

The number of teachers was multiplied by the average salary and then divided by current expenditures for every school year from 1985-86 until 2010-11 (using the middle alternative projection for teachers, salaries, and current expenditures). The resulting value shows the portion of current expenditures that is spent on teacher salaries. The portion of current expenditures that goes toward teacher salaries has been in a slow downward trend, with the teacher salary share falling from 41 percent in 1985-86 to 38 percent in 1998-99. With the projected values, the portion of current expenditures that goes toward teacher salaries continues to fall slowly, falling to 31 percent in 2010-11. The results of this analysis indicate that the projections of these three time series are consistent.

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Projection Accuracy

This is the thirteenth consecutive year in which Projections of Education Statistics has contained projections of current expenditures and teacher salaries. The actual values of current expenditures and teacher salaries can be compared with the projected values in the previous editions to examine the accuracy of the models.

The projections from the various editions of Projections of Education Statistics were placed in 1981-82 dollars using the Consumer Price Indices that appeared in each edition.

In the earlier editions of Projections of Education Statistics, average daily attendance rather than fall enrollment had been 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 are presented in all of these earlier editions. Hence, the projected values of both current expenditures per pupil in fall enrollment and current expenditures per pupil in average daily attendance are compared to their respective actual values.

The similar sets of independent variables have been used in the production of the current expenditure projections presented in the last eleven editions of the Projections of Education Statistics including this one. There have been some differences in the construction of the variables however. First, as noted, average daily attendance had been used in the previous editions rather than fall. Second, with the Projections of Education Statistics to 1997-98, calendar year data were used for disposable income, the population, and the Consumer Price Index. With the later editions, school year data were used. Third, there have been two revisions in the disposable income time series. Fourth, in the more recent editions, including this one, the Census Bureau's July 1 number for the population has been used. In the earlier editions, an average of the quarterly values was used. Fifth, in the more recent editions, the U.S. Bureau of the Census's population projections have been used. In the earlier editions, the population projections came from an economic consulting firm.

There has also been a change in the estimation procedure. In the more recent editions, the AR1 model for correcting for autocorrelation was used to estimate the model. In the earlier editions, ordinary least squares was used to estimate the model.

There are several commonly used statistics which can be used to evaluate projections. The values for one of these, the mean absolute percentage error (MAPE), are presented in table A2. 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.

To calculate the MAPEs presented in table A2, the projections of each variable were first grouped by lead time, that is: all the projections of each variable that were a given number of years from the last year in the sample period were grouped together. Next, the percent differences between each projection and its actual value were calculated. Finally, for each variable, the mean of the absolute values of the percent differences were calculated, with a separate average for each lead time. These means are the MAPEs. Hence, in table B, there are a series of MAPEs for each variable with a different MAPE for each lead time.

For some editions of the Projections of Education Statistics, the first projection to be listed did not have a lead time of one year. For example, in Projections of Education Statistics to 2002, the first projection to appear was for 1990-91. This projection was calculated using a sample period ending in 1988-89, so it had a lead time of two years. The value that appeared for 1989-1990 was from NCES Early Estimates. Only those projections which appeared in an edition of Projections of Education Statistics were used in this evaluation.

Projections for teacher salaries also appeared in the twelve most recent editions of Projections of Education Statistics. In these earlier editions, average daily attendance rather than fall enrollment had been used as the measure of enrollment. Also, beginning with the Projections of Education Statistics to 2006, there was one major change in the model used for teacher salary projections; all the variables were placed in log form. With this change in functional form, there was also a change in the way the change in enrollment was measured. In the most recent editions, the change in enrollment was measured by taking the ratio of the enrollment (previously average daily attendance) lagged one period to the enrollment lagged two periods. In the previous three editions of Projections of Education Statistics, the change in enrollment was measured by the change from the previous year in enrollment lagged one period. In Projections of Education Statistics to 1997-98, Projections of Education Statistics to 2000, and Projections of Education Statistics to 2001, both the change in average daily attendance lagged one period and the change in average daily attendance lagged two periods were included in the model.

There was another difference between the model used to produce the teacher salary projections in Projections of Education Statistics to 1997-98 and those used in the later editions including this one: variables in the model were calculated using calendar year data for the population and the Consumer Price Index rather than school year data as in previous editions.

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Sources of Past and Projected Data

Numbers from several different sources were used to produce these projections. 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 1959-60 to 1975-76, the numbers for current expenditures were taken from various issues of Statistics of State School Systems, published by NCES. The numbers for the school years ending in odd numbers during the 1960s were taken from various issues of the National Education Association's Estimates of School Statistics. 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 1998-99, the numbers were taken 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 numbers 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 Bureau of the Census's F-33 which offers statistics at the district level. This level of 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. For 1978-79, the number was taken from Revenues and Expenditures for Public Elementary and Secondary Education.

Projections for average daily attendance for the period from 1998-99 to 2010-11 were made by multiplying the projections for enrollment by the average value of the ratios of average daily attendance to the enrollment from 1988-89 to 1997-98; this average value was approximately 0.93.

The values for fall enrollment from 1959-60 to 1977-78 were taken from issues of the NCES publication Statistics of Public Elementary and Secondary Schools. The 1978-79 value was taken from the NCES Bulletin of October 23, 1979, "Selected Public and Private Elementary and Secondary Education Statistics." The values from 1979-80 to 1998-99 were taken from the NCES Common Core of Data survey. The projections for fall enrollment are those presented in Chapter 1.

For 1959-60 to 1998-99, the sources for revenue receipts 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 receipts from state sources are outlined above.

The estimates for average teacher salaries were taken from various issues of the National Education Association's Estimates of School Statistics.

The projected values for disposable income, personal taxes and nontax receipts to state and local governments, and indirect business taxes and tax accruals to state and local governments, were developed using projections developed by DRIWEFA's U.S. Quarterly Model. Projected values of the Bureau of Labor Statistics' Consumer Price Index for all urban consumers, which was used for adjusting current expenditures, teacher salaries, revenue receipts from state sources, and the state revenue variables, were also developed using the U.S. Quarterly Model.

Both the historical and projected values for the population were supplied by the U.S. Bureau of the Census.

The values of all the variables from DRIWEFA 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. As projections of the price index are required for placing the forecasts into current dollars, and as there are no projections of the Elementary and Secondary School Price Index, the Consumer Price Index was used. There are other price indexes, such as the implicit price deflator for state and local government purchases, that could have been used instead of the Consumer Price Index. These alternatives would have produced somewhat different projections.

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Footnotes

*For a review and discussion of this literature, see Inman, R. P. (1979), ''The fiscal performance of local governments: An Interpretive Review,'' in Current Issues in Urban Economics, edited by P. Mieszkowski and M. Straszheim, Johns Hopkins Press, Baltimore, Maryland.