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.
The 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 tast
es 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(ADAPOP)
here:
ln indicates the natural log;
CUREXP equals current expenditures of public elementary and secondary schools per pupil in average daily attendance in constant 1982-84 dollars;
PCI equals disposable income per capita in constant 1992 dollars;
SGRNT equals local governments' education revenue receipts from state sources, per capita, in constant 1982-84 dollars; and
ADAPOP equals the ratio of average daily attendance 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 seventh 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 sample period was from 1959-60 to 1997-98.
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 ADAPOP 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 ADAPOP. 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 ADAPOP held constant, would result in an increase of current expenditures per pupil in average daily attendance of approximately 0.48 percent. With PCI and SGRNT held constant, an increase of 1 percent in ADAPOP would result in a decrease in current expenditures per pupil in average daily attendance of approximately 0.38 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 some of the previous editions of Projections of Education Statistics. First, as with the previous edition, 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 (either Standard and Poor's DRI or the WEFA Group) estimated population numbers of each quarter in that school year. Second, 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 average daily attendance by projections for average daily attendance. The projections for total current expenditures were divided by projections for fall enrollment to produce projections of current expenditures per pupil in fall enrollment. Projections were developed in 1982-84 dollars and then placed in 1998-99 dollars using the Consumer Price Index. Current-dollar projections were produced by multiplying the constant-dollar projections by projections for the Consumer Price Index.
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 Standard & Poor's DRI (DRI) for use on its U.S. Quarterly Model. The U.S. Quarterly model is an econometric model of the U.S. economy developed by DRI for the personal computer which projects more than 1,200 economic concepts. Periodically, DRI supplies alternative scenarios of the economy, including long-term scenarios. The February 2000 series of long-term scenarios was used for the three sets of alternative economic projections used here.
DRI's trend scenario was used as a base for the middle alternative projections of the economic variables. DRI'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.
DRI's February 2000 pessimistic scenario was used for the low alternative projections and DRI's February 2000 optimistic scenario was used for the high alternative projections.
In the middle alternative projections, disposable income per capita rises each year from 2000-01 to 2009-10 at rates between 1.8 percent and 2.7 percent. In the low alternative projections, disposable income per capita ranges between 0.5 percent and 2.4 percent, and in the high alternative projections, disposable income per capita rises at rates between 2.6 percent and 3.9 percent.
The alternative projections for revenue receipts from state sources were produced using the following model:
ln(SGRNT) = b0 + b1ln(PERTAX1)
+ b2ln(ADAPOP)
+ 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;
ADAPOP equals the ratio of average daily attendance 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 sample period was from 1960-61 to 1997-98. 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 ADAPOP), so does the amount of aid going to education. Finally, in years with rapidly increasing inflation (higher RCPIANN/RCPIANN1), the real dollar values of revenue receipts from state governments to local governments would fall, other things being equal.
This is the fourth edition of the Projections of Education Statistics in which this model has been used to create projections of SGRNT. The model used in Projections of Education Statistics to 2006 was identical to the model used in this edition 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 0.1 percent and 3.3 percent. In the low set of projections, personal taxes and nontax receipts increase at rates between -2.0 percent and 2.8 percent. In the high set of projections, personal taxes and nontax receipts increase at rates between 0.8 percent and 4.4 percent.
In the middle set of projections, revenue receipts from state sources increase at rates between -0.5 percent and 2.6 percent for the period from 2000-01 to 2009-10. In the low set of projections, they increase at rates between -1.7 percent and 2.5 percent. In the high set of projections, they increase at rates between 0.1 percent and 2.7 percent.
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(ADAPOP)
+ b3ln(ADA1/ADA2)
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 average daily attendance in constant 1982-84 dollars;
ADAPOP equals the ratio of average daily attendance to the population;
ADA1 equals the average daily attendance lagged 1 period; and
ADA2 equals the average daily attendance lagged 2 periods.
The model was estimated using the period from 1959-60 to 1997-98 as a sample period. 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.
While there are values for teacher salaries through 1998-99, the model was estimated using the period from 1959-60 to 1997-98 as there are values for current expenditures only through 1997-98. The actual values for teacher salaries for 1996-97 and 1997-98, not those estimated using the model, appear in table 36. The projected values for teacher salaries for the projection period from 1998-99 to 2008-09 also are not the numbers which appear in table 36. Rather, three new sets of projections for teacher salaries were calculated using the projected percent changes produced by the model.
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 ADAPOP and ADA1/ADA2), demand for teachers may increase, so salaries may increase.
This model was also used to produce the projections of teacher salaries presented in the Projections of Education Statistics to 2009, Projections of Education Statistics to 2008, Projections of Education Statistics to 2007 and the Projections of Education Statistics to 2006. In 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 ADAPOP and ADA 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 1984-85 until 2009-10 (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 40 percent in 1984-85 to 38 percent in 1997-98. With the projected values, the portion of current expenditures that go toward teacher salaries continues to fall slowly, falling to 32 percent in 2009-10. The results of this analysis indicate that the projections of these three time series are consistent.
This is the twelth 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.
The same set of independent variables has 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, with the Projections of Education Statisticsto 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. Second, there have been two revisions in the disposable income time series. Third, there have been two changes to the population variable. 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. Also 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, either DRI or the WEFA Group.
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 A5.2. MAPEs are presented for total current expenditures, current expenditures per pupil in average daily attendance, and teacher salaries.
To calculate the MAPEs presented in table A5.2, 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 A5.2, 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.
Some of the differences between the actual values and the projected values for current expenditures and current expenditures per pupil are due to the change in the survey form for current expenditures that took place in 1988-89. The results of the crosswalk study suggest that values for current expenditures as presently collected are approximately 1.4 percent higher than they would have been if no change had been made. If the projections for 1988-89, 1989-90, and 1990-91 which appeared in Projections of Education Statistics to 1997-98, Projections of Education Statistics to 2000, Projections of Education Statistics to 2001: An Update, are increased by 1.4 percent, some MAPEs decrease. MAPEs for current expenditures and current expenditures per pupil after this adjustment has been made can also be found in table A5.2.
Projections for teacher salaries also appeared in the eleven most recent editions of Projections of Education Statistics. 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 average daily attendance lagged one period to the average daily attendance 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 average daily attendance 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.
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 1995-96, 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 2009-10 were made by multiplying the projections for enrollment by the average value of the ratios of average daily attendance to the enrollment from 1986-87 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 1996-97 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 1997-98, 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 DRI'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 DRI 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.
